{"entry_id": "36dd2f7b-f877-44fd-8c5e-b65261b20dd6", "infos": [{"txt": "Electron-Enabled Nanoparticle Difraction", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 0, "bbox": [[0.29, 0.119, 0.709, 0.133]]}]}, "tags": ["title"], "label": "article_title", "web_segment_id": 5, "global_sentence_id": 0, "edu_l1_label": "BOT"}, {"txt": "Stefan Nimmrichter,1, ∗Dennis R¨atzel,2, 3 Isobel C. Bicket,3, 4 Michael S. 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{"txt": "TU Wien，Wiedner Hauptstraβe 8-10/E057-02，1040 Wien, Austria", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 500000, "bbox": [[0.263, 0.227, 0.739, 0.24]]}]}, "tags": ["text"], "label": "author", "web_segment_id": 16, "global_sentence_id": 7, "edu_l1_label": "EDU_O"}, {"txt": "V", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 600000, "bbox": [[0.032, 0.305, 0.048, 0.313]]}]}, "tags": ["text"], "label": "O", "web_segment_id": 14, "global_sentence_id": 8, "edu_l1_label": "EDU_O"}, {"txt": "023", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 600000, "bbox": [[0.027, 0.311, 0.058, 0.339]]}]}, "tags": ["text"], "label": "O", "web_segment_id": 20, "global_sentence_id": 9, "edu_l1_label": "EDU_O"}, {"txt": "一", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": 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"global_sentence_id": 13, "edu_l1_label": "EDU_O"}, {"txt": "February_20,2025)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 700000, "bbox": [[0.404, 0.238, 0.594, 0.254]]}]}, "tags": ["text"], "label": "author", "web_segment_id": 15, "global_sentence_id": 14, "edu_l1_label": "EDU_O"}, {"txt": "We propose a scheme for generating high-mass quantum superposition states of an optically pre-cooled, levitated nanoparticle through electron difraction at its sub-nanometer crystal lattice.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.181, 0.261, 0.834, 0.272], [0.165, 0.274, 0.834, 0.284]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 15, "edu_l1_label": "BOS"}, {"txt": "When a single electron undergoes Bragg difraction at a free-falling nanoparticle, momentum conservation implies that the superposition of Bragg momenta is imprinted onto the relative coordinate between electron and nanoparticle, which entangles their wavefunctions.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.165, 0.286, 0.834, 0.297], [0.165, 0.299, 0.834, 0.309], [0.165, 0.311, 0.66, 0.322]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 16, "edu_l1_label": "IOS"}, {"txt": "By imaging the electron interferogram, one maps the nanoparticle state onto a superposition of Bragg momenta, as if it was difracted by its own lattice.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.66, 0.311, 0.834, 0.322], [0.165, 0.323, 0.834, 0.334], [0.165, 0.336, 0.361, 0.347]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 17, "edu_l1_label": "IOS"}, {"txt": "This results in a coherent momentum splitting approximately 1000 times greater than what is achievable with two-photon recoils in conventional standing-wave gratings.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.361, 0.336, 0.834, 0.347], [0.165, 0.348, 0.834, 0.359], [0.165, 0.361, 0.196, 0.371]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 18, "edu_l1_label": "IOS"}, {"txt": "Self-interference of the nanoparticle can thus be observed within drastically shorter free-fall times in a time-domain Talbot interferometer confguration, signifcantly relaxing source requirements and alleviating decoherence from environmental factors such as residual gas and thermal radiation.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.196, 0.361, 0.834, 0.371], [0.165, 0.373, 0.834, 0.384], [0.165, 0.386, 0.834, 0.396], [0.165, 0.398, 0.231, 0.409]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 19, "edu_l1_label": "IOS"}, {"txt": "Shorter interference times also allow for a recapture of the nanoparticle within its initial trapping volume, facilitating its reuse in many rapid experimental duty cycles.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.231, 0.398, 0.834, 0.409], [0.165, 0.41, 0.714, 0.421]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 20, "edu_l1_label": "IOS"}, {"txt": "This opens new possibilities for experimental tests of macroscopic quantum efects within a transmission electron microscope.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 800000, "bbox": [[0.714, 0.41, 0.834, 0.421], [0.165, 0.423, 0.834, 0.433], [0.165, 0.435, 0.244, 0.446]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 21, "edu_l1_label": "IOS"}, {"txt": "I.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 900000, "bbox": [[0.19, 0.472, 0.202, 0.483]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 7, "global_sentence_id": 22, "edu_l1_label": "BOS"}, {"txt": "INTRODUCTION", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 900000, "bbox": [[0.22, 0.472, 0.366, 0.483]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 7, "global_sentence_id": 23, "edu_l1_label": "IOS"}, {"txt": "Matter-wave interferometry with massive objects challenges our understanding of the quantum-classical transition and is expected to provide necessary experimental insights into quantum gravity [1–8].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1000000, "bbox": [[0.088, 0.502, 0.485, 0.514], [0.071, 0.515, 0.485, 0.527], [0.071, 0.529, 0.485, 0.541], [0.071, 0.543, 0.362, 0.554]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 24, "edu_l1_label": "IOS"}, {"txt": "State-of-the-artnear-feld setups have demonstrated interference for particles up to 104 amu [9, 10] and up to 103 amu in the time domain [11].While standard quantum theory imposes no fundamental limits on particle size, alternative theories suggest a suppression of macroscopic superpositions, calling for experimental tests [12–14].The use of optically cooled, highly controllable nanoparticles presents a promising platform for such experiments [15–22].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1000000, "bbox": [[0.362, 0.543, 0.485, 0.554], [0.071, 0.556, 0.485, 0.568], [0.071, 0.57, 0.485, 0.582], [0.071, 0.583, 0.485, 0.595], [0.071, 0.597, 0.485, 0.609], [0.071, 0.611, 0.485, 0.623], [0.071, 0.624, 0.356, 0.636], [0.371, 0.624, 0.485, 0.636], [0.071, 0.638, 0.485, 0.65], [0.071, 0.651, 0.451, 0.663]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 25, "edu_l1_label": "IOS"}, {"txt": "Al-though numerous proposals have highlighted strategies for high-mass interferometry [3, 23–31], experimental re-alization still remains a challenge and hinges on innovative techniques to realize coherent matter-wave difraction, reduce environmental disturbances, lower the interference time, and improve experimental stability and repetition rates.While most approaches rely on optical felds as difractive elements for matter waves, we propose an Electron-Enabled Nanoparticle Difraction (END) scheme that exploits the underlying atomic structure of a nanoparticle through high-resolution electron imaging.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1000000, "bbox": [[0.451, 0.651, 0.485, 0.663], [0.071, 0.665, 0.485, 0.677], [0.071, 0.679, 0.485, 0.691], [0.071, 0.692, 0.485, 0.704], [0.071, 0.706, 0.485, 0.718], [0.071, 0.72, 0.485, 0.731], [0.071, 0.733, 0.485, 0.745], [0.071, 0.747, 0.485, 0.759], [0.071, 0.76, 0.485, 0.772], [0.071, 0.774, 0.485, 0.786], [0.071, 0.788, 0.485, 0.799], [0.071, 0.801, 0.485, 0.813], [0.071, 0.815, 0.134, 0.827]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 26, "edu_l1_label": "IOS"}, {"txt": "In efect, the particle can be made to difract of", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1000000, "bbox": [[0.134, 0.815, 0.485, 0.827]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 27, "edu_l1_label": "IOS"}, {"txt": "庄", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1100000, "bbox": [[0.029, 0.375, 0.056, 0.393]]}]}, "tags": ["text"], "label": "O", "web_segment_id": 10, "global_sentence_id": 28, "edu_l1_label": "EDU_O"}, {"txt": "table", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1100000, "bbox": [[0.512, 0.469, 0.927, 0.631]]}]}, "tags": ["table"], "label": "table", "web_segment_id": 2, "global_sentence_id": 29, "edu_l1_label": "EDU_O"}, {"txt": "TABLE I. Talbot times and typical free-fall distances for the interference of diferent nanoparticle masses considered in recent publications [15–20, 25] at the exemplary grating periodd = 192 pm considered here.We require that the particle free-falls over twice the Talbot time to observe interference fringes. The short free-fall distances facilitate a recapture of the particle within a single trap volume.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1200000, "bbox": [[0.511, 0.638, 0.929, 0.728]]}]}, "tags": ["table_caption"], "label": "table_title", "web_segment_id": 6, "global_sentence_id": 30, "edu_l1_label": "EDU_O"}, {"txt": "its own crystal lattice, resulting in drastically lower interference times and experimental requirements than other approaches.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1300000, "bbox": [[0.515, 0.762, 0.928, 0.774], [0.515, 0.776, 0.928, 0.788], [0.515, 0.789, 0.6, 0.801]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 31, "edu_l1_label": "IOS"}, {"txt": "Table I lists the required free-fall times and distances for nanoparticles of various sizes to interfere, given the exemplary difraction period of 192 pm.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1300000, "bbox": [[0.6, 0.789, 0.928, 0.801], [0.515, 0.803, 0.928, 0.815], [0.515, 0.817, 0.875, 0.829]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 32, "edu_l1_label": "IOS"}, {"txt": "The END approach takes inspiration from the frst matter-wave experiments by Davisson and Germer [32] demonstrating elastic Bragg difraction of electrons at the atomic lattice structure of a crystalline specimen.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1400000, "bbox": [[0.531, 0.834, 0.928, 0.846], [0.515, 0.848, 0.928, 0.86], [0.515, 0.861, 0.928, 0.873], [0.515, 0.875, 0.879, 0.887]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 33, "edu_l1_label": "IOS"}, {"txt": "If the", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1400000, "bbox": [[0.879, 0.875, 0.928, 0.887]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 34, "edu_l1_label": "IOS"}, {"txt": "footer", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1500000, "bbox": [[0.072, 0.86, 0.294, 0.883]]}]}, "tags": ["footer"], "label": "O", "web_segment_id": -1, "global_sentence_id": 35, "edu_l1_label": "EDU_O"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1500000, "bbox": [[0.916, 0.088, 0.931, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 36, "edu_l1_label": "EDU_O"}, {"txt": "Bragg condition is met for a given period d of lattice planes, the electron wavefunction splits into a superposition of difraction components separated by multiples of the (mass- and velocity-independent) Bragg momentum pd = h/d, where h = 2πℏdenotes Planck’s con-stant.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1500000, "bbox": [[0.071, 0.121, 0.485, 0.133], [0.071, 0.134, 0.485, 0.146], [0.071, 0.148, 0.485, 0.16], [0.071, 0.162, 0.485, 0.173], [0.071, 0.175, 0.485, 0.187], [0.071, 0.189, 0.113, 0.201]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 37, "edu_l1_label": "IOS"}, {"txt": "These Bragg components would show up as dis tinct bright spots on a detection screen in the far feld (Fourier plane) or they could be fltered and refocused to form d-periodic interference fringes on a farther image plane.Crucially, momentum conservation dictates that for each Bragg momentum imparted on the electron, the crystal particle receives a recoil of equal magnitude and opposite sign.In principle, Bragg difraction in a selected spatial direction can thus generate EPR-like entanglement as it maps product wavefunctions of electron and particle, ψ(x)Ψ(X), to a superposition of states thatare momentum-shifted in the relative coordinate x −X,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1500000, "bbox": [[0.113, 0.189, 0.479, 0.201], [0.071, 0.202, 0.485, 0.214], [0.071, 0.216, 0.485, 0.228], [0.071, 0.23, 0.485, 0.241], [0.071, 0.243, 0.485, 0.255], [0.071, 0.257, 0.485, 0.269], [0.071, 0.27, 0.485, 0.282], [0.071, 0.284, 0.485, 0.296], [0.071, 0.298, 0.485, 0.31], [0.071, 0.311, 0.485, 0.323], [0.071, 0.325, 0.485, 0.337], [0.071, 0.339, 0.482, 0.35]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 38, "edu_l1_label": "IOS"}, {"txt": " ψ(x)Ψ(X) →Xfn exp npd(x X) ψ(x)Ψ(X).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1600000, "bbox": [[0.073, 0.359, 0.488, 0.397]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 10, "global_sentence_id": 39, "edu_l1_label": "IOS"}, {"txt": "(1)ℏn", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1600000, "bbox": [[0.073, 0.359, 0.488, 0.397]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 10, "global_sentence_id": 40, "edu_l1_label": "IOS"}, {"txt": "By detecting the electron position x on the image plane, where the Bragg orders interfere, one efectively erases which-way information and projects the particle state onto a phase-shifted superposition of Bragg-difracted components,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1700000, "bbox": [[0.071, 0.408, 0.485, 0.42], [0.071, 0.422, 0.485, 0.434], [0.071, 0.435, 0.485, 0.447], [0.071, 0.449, 0.485, 0.461], [0.071, 0.463, 0.163, 0.475]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 41, 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"web_segment_id": 6, "global_sentence_id": 48, "edu_l1_label": "IOS"}, {"txt": "The outcome looks as if the particle had been difracted of a grating with a period d given by the particle’s own crystal lattice.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1900000, "bbox": [[0.219, 0.532, 0.485, 0.544], [0.071, 0.546, 0.485, 0.558], [0.071, 0.56, 0.319, 0.571]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 49, "edu_l1_label": "IOS"}, {"txt": "Interference betweenthe components can be observed after an additional free evolution time on the order of the Talbot time, TM = Md2/h, which grows with the particle mass M.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 1900000, "bbox": [[0.319, 0.56, 0.485, 0.571], [0.071, 0.573, 0.485, 0.585], [0.071, 0.587, 0.485, 0.599], [0.071, 0.6, 0.42, 0.612]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 50, "edu_l1_label": "IOS"}, {"txt": "The coherent recoils and their said implications are typically of no relevance in Bragg spectroscopy or in electron imaging of massive (often fxed) crystal samples.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2000000, "bbox": [[0.088, 0.614, 0.485, 0.626], [0.071, 0.628, 0.485, 0.64], [0.071, 0.642, 0.485, 0.653]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 51, "edu_l1_label": "IOS"}, {"txt": "However, they can have a sizable efect on levitated, motionally cooled nanoparticles, which have become available only recently in a mass range of M ∼106 −1012amu [15–20].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2000000, "bbox": [[0.071, 0.655, 0.485, 0.667], [0.071, 0.669, 0.485, 0.681], [0.071, 0.682, 0.481, 0.689], [0.071, 0.696, 0.164, 0.708]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 52, "edu_l1_label": "IOS"}, {"txt": "In fact, the Bragg momenta here are abouta thousand times greater than the difraction momenta of optical grating structures in existing proposals for highmass interferometers [23–25, 28, 30], which implies a dras-tic reduction of the required free evolution times by a million for a given mass.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2000000, "bbox": [[0.164, 0.696, 0.485, 0.708], [0.071, 0.71, 0.485, 0.721], [0.071, 0.723, 0.485, 0.735], [0.071, 0.737, 0.485, 0.749], [0.071, 0.75, 0.485, 0.762], [0.071, 0.764, 0.25, 0.776]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 53, "edu_l1_label": "IOS"}, {"txt": "Having said that, the realisation of the efective grating transformation (2) requires a precisely timed coherent single-electron pulse to hit the particle and a postselection scheme that flters out all Bragg components other than the multiples of pd in the electron state.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2100000, "bbox": [[0.088, 0.778, 0.485, 0.79], [0.071, 0.792, 0.485, 0.803], [0.071, 0.805, 0.485, 0.817], [0.071, 0.819, 0.485, 0.831], [0.071, 0.832, 0.434, 0.844]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 54, "edu_l1_label": "IOS"}, {"txt": "Moreover, since the superposition in (2) varies in phase with the measured electron position x, the measurement resolution must be better than the Angstrom-sized period", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2100000, "bbox": [[0.434, 0.832, 0.485, 0.844], [0.071, 0.846, 0.485, 0.858], [0.071, 0.86, 0.485, 0.871], [0.071, 0.873, 0.485, 0.885]]}]}, "tags": ["text"], 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Otherwise, the interference contrast will be reduced.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2100000, "bbox": [[0.515, 0.121, 0.928, 0.133]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 56, "edu_l1_label": "IOS"}, {"txt": "Transmission electron microscopy (TEM) is expected to meet these challenges in the near future; current TEMs already enable spatial resolutions <50 pm [33–36] withhighly coherent illumination [37], imaging on the micrometer scale [38], temporal control on the sub-picosecond scale [39–41], few-µrad or better resolution of difractionangles [42], and near-unitary detection efciency [43].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2100000, "bbox": [[0.515, 0.134, 0.928, 0.146], [0.515, 0.148, 0.928, 0.16], [0.515, 0.162, 0.928, 0.173], [0.515, 0.175, 0.928, 0.187], [0.515, 0.189, 0.928, 0.201], [0.515, 0.202, 0.928, 0.214], [0.515, 0.216, 0.905, 0.228]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 57, "edu_l1_label": "IOS"}, {"txt": "II.PROPOSED EXPERIMENT", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2200000, "bbox": [[0.588, 0.258, 0.854, 0.268]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 9, "global_sentence_id": 58, "edu_l1_label": "BOS"}, {"txt": "The proposed experimental sequence illustrated in Fig.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.531, 0.288, 0.928, 0.299], [0.515, 0.301, 0.543, 0.313]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 59, "edu_l1_label": "IOS"}, {"txt": "1 adopts the basic interference scheme of Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.543, 0.301, 0.891, 0.313]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 60, "edu_l1_label": "IOS"}, {"txt": "[25], but with signifcant modifcations.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.891, 0.301, 0.928, 0.313], [0.515, 0.315, 0.774, 0.327]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 61, "edu_l1_label": "IOS"}, {"txt": "The experiment is conducted within an ultra-fast transmission electron microscope and utilizes pulsed beams of single electrons that can be imaged with sub-atomic resolution.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.79, 0.315, 0.928, 0.327], [0.515, 0.328, 0.928, 0.34], [0.515, 0.342, 0.928, 0.354], [0.515, 0.356, 0.834, 0.367]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 62, "edu_l1_label": "IOS"}, {"txt": "In the frst stage (a), a nanoparticle is captured and cooled, e.g., in an optical dipole trap [15, 44] or ion trap [19, 45].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.834, 0.356, 0.928, 0.367], [0.515, 0.369, 0.928, 0.381], [0.515, 0.383, 0.889, 0.395]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 63, "edu_l1_label": "IOS"}, {"txt": "The position of the particle is measured and, e.g., feedback or cavity cooling is applied to further localise the nanoparticle state.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.889, 0.383, 0.928, 0.395], [0.515, 0.396, 0.928, 0.408], [0.515, 0.41, 0.928, 0.422], [0.515, 0.424, 0.578, 0.435]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 64, "edu_l1_label": "IOS"}, {"txt": "The trap thus serves as a point-like matter-wave source.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2300000, "bbox": [[0.578, 0.424, 0.928, 0.435], [0.515, 0.437, 0.565, 0.449]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 65, "edu_l1_label": "IOS"}, {"txt": "After release from the trap, the nanoparticle evolves freely for a time t0, before (b) a triggered single-electron pulse hits the particle and difracts of its crystal lattice.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.531, 0.451, 0.928, 0.463], [0.515, 0.465, 0.928, 0.477], [0.515, 0.478, 0.928, 0.49]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 66, "edu_l1_label": "IOS"}, {"txt": "The momentum state of the electron thus splits into distinct difraction components separated by discrete Bragg momenta, each of which imparts an equal momentum recoil on the particle in the opposite direction.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.515, 0.492, 0.928, 0.504], [0.515, 0.506, 0.928, 0.517], [0.515, 0.519, 0.928, 0.531], [0.515, 0.533, 0.85, 0.545]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 67, "edu_l1_label": "IOS"}, {"txt": "A chosen Bragg momentum pd and multiples thereof are then postselected with the help of a pinhole mask placed in the back focal plane (BFP) of an objective lens (OL), which blocks the undifracted electron state and any Bragg component other than npd in a given spatial direction (xaxis) [46].To this end, one must align the particle’scrystal lattice accordingly.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.85, 0.533, 0.928, 0.545], [0.515, 0.546, 0.928, 0.558], [0.515, 0.56, 0.928, 0.572], [0.515, 0.574, 0.928, 0.585], [0.515, 0.587, 0.928, 0.599], [0.515, 0.601, 0.928, 0.613], [0.515, 0.614, 0.928, 0.626], [0.515, 0.628, 0.71, 0.64]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 68, "edu_l1_label": "IOS"}, {"txt": "The selected Bragg components are allowed to interfere on an image plane further down the beam line, where the electron position x is measured.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.71, 0.628, 0.928, 0.64], [0.515, 0.642, 0.928, 0.653], [0.515, 0.655, 0.928, 0.667], [0.515, 0.669, 0.559, 0.681]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 69, "edu_l1_label": "IOS"}, {"txt": "At perfect resolution, this approximately projects a pure centre-of-mass state onto the post-measurement state (2), equivalent to the efect of a difraction grating of period d. See Appendix A for a detailed derivation.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.559, 0.669, 0.928, 0.681], [0.515, 0.682, 0.928, 0.694], [0.515, 0.696, 0.928, 0.708], [0.515, 0.71, 0.892, 0.722]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 70, "edu_l1_label": "IOS"}, {"txt": "The nanoparticle can be assumed at rest during this process, which takes a few nanoseconds.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.892, 0.71, 0.928, 0.722], [0.515, 0.723, 0.928, 0.735], [0.515, 0.737, 0.742, 0.749]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 71, "edu_l1_label": "IOS"}, {"txt": "Finally, the nanoparticle evolves for another time t before (c) its centre-of-mass position X is measured and it is recaptured in the original trap for the next run of the sequence.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.742, 0.737, 0.928, 0.749], [0.515, 0.751, 0.928, 0.762], [0.515, 0.764, 0.928, 0.776], [0.515, 0.778, 0.797, 0.79]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 72, "edu_l1_label": "IOS"}, {"txt": "We discard runs in which the electron is not detected.Over many cycles, the measured position distribution exhibits interference fringes shifted with respect to the electron position x, which can be calculated using standard phase-space methods; see Appendix B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2400000, "bbox": [[0.797, 0.778, 0.928, 0.79], [0.515, 0.791, 0.928, 0.803], [0.515, 0.805, 0.928, 0.817], [0.515, 0.819, 0.928, 0.83], [0.515, 0.832, 0.928, 0.844], [0.515, 0.846, 0.707, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 73, "edu_l1_label": "IOS"}, {"txt": "Figure 2 depicts exemplary interference fringe patterns we predict assuming perfect measurement resolu-", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2500000, "bbox": [[0.531, 0.86, 0.928, 0.871], [0.515, 0.873, 0.928, 0.885]]}]}, "tags": ["text"], "label": "figure_title", "web_segment_id": 7, "global_sentence_id": 74, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2600000, "bbox": [[0.915, 0.088, 0.932, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 75, "edu_l1_label": "EDU_O"}, {"txt": "figure", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2600000, "bbox": [[0.108, 0.112, 0.889, 0.47]]}]}, "tags": ["figure"], "label": "figure", "web_segment_id": 2, "global_sentence_id": 76, "edu_l1_label": "EDU_O"}, {"txt": "FIG. 1. Proposed scheme of electron-enabled nanoparticle difraction consisting of three steps: (a) a nanoparticle of mass M is cooled close to its motional ground state in, e.g., an optical trap, acting as a highly localised matter wave source released into free fall when the trap is switched of. After a sufcient buildup of coherent delocalisation over the time t0, (b) a triggered single-electron wave packet impinges and Bragg-difracts of the particle’s lattice structure. As each imparted Bragg momentumcomes with an equivalent recoil, the wavefunctions of particle and electron are now entangled. The electron passes a mask on the back focal plane (BFP) of an objective lens (OL), which selects Bragg orders corresponding to a lattice period d (Inset: difraction image of a silicon crystal with selected Bragg orders of periodicity d = 192 pm used in our case study). The selected orders are recombined on an image plane by the projector lens (PL) system and an energy flter is used to exclude inelastic events. The detector at the image plane records the electron’s position x. This efectively maps the particle wavefunction into anx-dependent superposition of Bragg momenta. They are allowed to interfere over another free-fall time t, before (c) the position X is measured and the particle re-trapped. Given free-fall times of at least one Talbot time, t, t0 ≳TM, stable interferencefringes of magnifed period D = d(1 + t/t0) in the relative coordinate X −xD/d will form over many valid repetitions (i.e.,whenever the electron is detected).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2700000, "bbox": [[0.069, 0.478, 0.934, 0.645]]}]}, "tags": ["figure_caption"], "label": "figure_title", "web_segment_id": 3, "global_sentence_id": 77, "edu_l1_label": "EDU_O"}, {"txt": "tion.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.071, 0.671, 0.105, 0.683]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 78, "edu_l1_label": "IOS"}, {"txt": "The pattern is given relative to the measured electron position x and would be smeared out accordingly at fnite resolution.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.113, 0.671, 0.485, 0.683], [0.071, 0.684, 0.485, 0.696], [0.071, 0.698, 0.217, 0.71]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 79, "edu_l1_label": "IOS"}, {"txt": "In our case study, we consider a silicon nanoparticle of mass M = 2 × 109 amu and thetrap parameters of Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.233, 0.698, 0.485, 0.71], [0.071, 0.712, 0.485, 0.723], [0.071, 0.725, 0.241, 0.737]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 80, "edu_l1_label": "IOS"}, {"txt": "[15], which results in an approximately pure Gaussian source state of standard deviation σX ≈1.4 pm.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.241, 0.725, 0.485, 0.737], [0.071, 0.739, 0.485, 0.751], [0.071, 0.752, 0.168, 0.764]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 81, "edu_l1_label": "IOS"}, {"txt": "Our mask shall consist of 4 pinholes select-ing the multiples n = ±1, ±2 of the Bragg order specifedby the Miller indices (110) in primitive-cell representation [i.e., (202) in the conventional cubic-cell notation].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.168, 0.752, 0.485, 0.764], [0.071, 0.766, 0.485, 0.778], [0.071, 0.78, 0.485, 0.791], [0.071, 0.793, 0.446, 0.805]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 82, "edu_l1_label": "IOS"}, {"txt": "The associated grating period is d = 192 pm, which demands that the pinholes be a few micrometres in size [46].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.446, 0.793, 0.485, 0.805], [0.071, 0.807, 0.485, 0.819], [0.071, 0.82, 0.455, 0.832]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 83, "edu_l1_label": "IOS"}, {"txt": "To ensure spatial coherence of the nanoparticle over one period, we let it evolve for one Talbot time before the electron interaction, t0 = TM ≈192 µs.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.455, 0.82, 0.485, 0.832], [0.071, 0.834, 0.485, 0.846], [0.071, 0.848, 0.485, 0.859], [0.071, 0.861, 0.332, 0.873]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 84, "edu_l1_label": "IOS"}, {"txt": "In (a), we show the", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.332, 0.861, 0.485, 0.873]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 85, "edu_l1_label": "IOS"}, {"txt": "interferogram of the recaptured nanoparticle after varying times t. The fringe period magnifes geometrically as D = d(1+t/t0).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.515, 0.671, 0.928, 0.683], [0.515, 0.684, 0.605, 0.696], [0.605, 0.684, 0.928, 0.696], [0.515, 0.698, 0.632, 0.71]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 86, "edu_l1_label": "IOS"}, {"txt": "Notice that the existence of fringes does not certify the quantum wave nature of the nanoparticle.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.632, 0.698, 0.928, 0.71], [0.515, 0.712, 0.928, 0.723], [0.515, 0.725, 0.539, 0.737]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 87, "edu_l1_label": "IOS"}, {"txt": "Treating the electron interaction stage as a classical grating aperture would result in the shadow pattern (b), and one cannot claim quantum interference whenever the patterns (a) and (b) coincide.Panel (c) compares the fringe patterns at t0, t = TM, where they difer the most.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.539, 0.725, 0.928, 0.737], [0.515, 0.739, 0.928, 0.751], [0.515, 0.752, 0.928, 0.764], [0.515, 0.766, 0.928, 0.778], [0.515, 0.78, 0.928, 0.791]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 88, "edu_l1_label": "IOS"}, {"txt": "To reveal the quantum fringes, the measurement resolution must be better than d/4 = 48 pm for the electron and D/4 = 96 pm for the nanoparticle, which are within reach [36, 45, 47, 48].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.515, 0.793, 0.928, 0.805], [0.515, 0.807, 0.928, 0.819], [0.515, 0.82, 0.928, 0.832], [0.515, 0.834, 0.674, 0.846]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 89, "edu_l1_label": "IOS"}, {"txt": "The short total interference time t+t0 = 384 µs amounts to a free-fall distance of less thana micrometre, which allows for recapture and thus a fast", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2800000, "bbox": [[0.674, 0.834, 0.928, 0.846], [0.515, 0.848, 0.928, 0.859], [0.515, 0.861, 0.928, 0.873]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 90, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2900000, "bbox": [[0.915, 0.088, 0.932, 0.101]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 91, "edu_l1_label": "EDU_O"}, {"txt": "figure", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 2900000, "bbox": [[0.068, 0.112, 0.935, 0.452]]}]}, "tags": ["figure"], "label": "figure", "web_segment_id": 5, "global_sentence_id": 92, "edu_l1_label": "EDU_O"}, {"txt": "FIG. 2. Exemplary fringe patterns for an aligned silicon nanocrystal of mass M = 2×109 amu, based on electron Bragg difractionat ±(1¯10), ±(2¯20) and plotted against the relative coordinate XxD/d with respect to the detected electron position x. The particle is released and expands freely for the time t0 = TM = 192− µs before the electron difraction. In (a), we plot the positiondistribution of the particle as a function of time t after difraction, normalised to its maximum value at each t. In (b), we show the hypothetical shadow pattern for a classical particle transmitted by a classical aperture. (c) Position distributions at t = TM [dotted lines in (a) and (b)] corresponding to quantum interference (red solid) and classical shadow fringes (black solid), in units relative to the maximum of the classical pattern. The dashed line indicates the Gaussian distribution of a freely evolved particle without difraction.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3000000, "bbox": [[0.069, 0.465, 0.932, 0.568]]}]}, "tags": ["figure_caption"], "label": "figure_title", "web_segment_id": 0, "global_sentence_id": 93, "edu_l1_label": "EDU_O"}, {"txt": "duty cycle.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3000000, "bbox": [[0.071, 0.594, 0.151, 0.606]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 94, "edu_l1_label": "IOS"}, {"txt": "III.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3100000, "bbox": [[0.101, 0.639, 0.127, 0.649]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 6, "global_sentence_id": 95, "edu_l1_label": "BOS"}, {"txt": "RELEVANT SYSTEMATIC EFFECTS", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3100000, "bbox": [[0.145, 0.639, 0.455, 0.649]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 6, "global_sentence_id": 96, "edu_l1_label": "IOS"}, {"txt": "Our exemplary analysis is carried out for a typical electron energy of 300 keV and a silicon nanoparticle in the shape of an oblate spheroid of radius RM = 109 nm and thickness 2bM = 60 nm.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.088, 0.669, 0.485, 0.681], [0.071, 0.683, 0.485, 0.695], [0.071, 0.696, 0.415, 0.71], [0.415, 0.696, 0.485, 0.708], [0.071, 0.71, 0.227, 0.722], [0.227, 0.71, 0.28, 0.722]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 97, "edu_l1_label": "IOS"}, {"txt": "This amounts to the mass of a particle for which ground-state cooling was already achieved [15], but our scheme can also be operated with larger particles.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.291, 0.71, 0.485, 0.722], [0.071, 0.724, 0.485, 0.735], [0.071, 0.737, 0.485, 0.749], [0.071, 0.751, 0.188, 0.763]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 98, "edu_l1_label": "IOS"}, {"txt": "The electrons shall have a Gaussian transverse profle with a 115 nm half-width-half-max spot size.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.206, 0.751, 0.485, 0.763], [0.071, 0.764, 0.485, 0.776], [0.071, 0.778, 0.102, 0.79]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 99, "edu_l1_label": "IOS"}, {"txt": "From this, we estimate the probability to detect the Bragg-fltered electron as Prdet ≈0.1%.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.102, 0.778, 0.485, 0.79], [0.071, 0.792, 0.366, 0.803]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 100, "edu_l1_label": "IOS"}, {"txt": "Temporal trig-gering suppresses unwanted detection events due to, e.g., cosmic rays.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.366, 0.792, 0.485, 0.803], [0.071, 0.805, 0.485, 0.817], [0.071, 0.819, 0.161, 0.831]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 101, "edu_l1_label": "IOS"}, {"txt": "The duty cycle of our proposed scheme is mainly constrained by the free evolution time, which can be as short as two Talbot times (see Fig.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.161, 0.819, 0.485, 0.831], [0.071, 0.832, 0.485, 0.844], [0.071, 0.846, 0.383, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 102, "edu_l1_label": "IOS"}, {"txt": "2).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.383, 0.846, 0.409, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 103, "edu_l1_label": "IOS"}, {"txt": "Particles lighter than 2.5 · 109 amu would fall less than 1 µm andcould be easily re-trapped within the same potential for", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.409, 0.846, 0.485, 0.858], [0.071, 0.86, 0.485, 0.871], [0.071, 0.873, 0.485, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 104, "edu_l1_label": "IOS"}, {"txt": "reuse in subsequent experiments, allowing for experimental repetition times of about 1 ms. Consequently, considering Prdet and the Poissonian nature of the electron production process, we estimate approximately 1000 successful experimental runs within one hour.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3200000, "bbox": [[0.515, 0.594, 0.928, 0.606], [0.515, 0.608, 0.774, 0.62], [0.788, 0.608, 0.928, 0.62], [0.515, 0.621, 0.928, 0.633], [0.515, 0.635, 0.928, 0.647], [0.515, 0.649, 0.825, 0.66]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 105, "edu_l1_label": "IOS"}, {"txt": "We assume that the electrons are only scattered once and elastically, neglecting both multi-scattering and inelastic scattering.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3300000, "bbox": [[0.531, 0.666, 0.928, 0.678], [0.515, 0.679, 0.928, 0.691], [0.515, 0.693, 0.642, 0.705]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 106, "edu_l1_label": "IOS"}, {"txt": "Multi-scattering can either enhance or suppress the amplitudes of certain Bragg peaks, calling for a detailed analysis based on the actual shape and size of the nanoparticle in a realisation of our proposal.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3300000, "bbox": [[0.642, 0.693, 0.928, 0.705], [0.515, 0.707, 0.928, 0.718], [0.515, 0.72, 0.928, 0.732], [0.515, 0.734, 0.878, 0.746]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 107, "edu_l1_label": "IOS"}, {"txt": "Given an inelastic mean free path in silicon of about 180 nm [49], unwanted decoherence due to inelastic scattering should be negligible in our case study.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3300000, "bbox": [[0.878, 0.734, 0.928, 0.746], [0.515, 0.747, 0.928, 0.759], [0.515, 0.761, 0.928, 0.773], [0.515, 0.775, 0.741, 0.786]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 108, "edu_l1_label": "IOS"}, {"txt": "To mitigate decoherence for larger particles, the electrons can also be post-selected according to the amount of energy they have lost.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3300000, "bbox": [[0.741, 0.775, 0.928, 0.786], [0.515, 0.788, 0.928, 0.8], [0.515, 0.802, 0.881, 0.814]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 109, "edu_l1_label": "IOS"}, {"txt": "Modern TEM setups with electron energy flters allow for an energy fltered imaging resolution of less than 250 meV [50, 51].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3300000, "bbox": [[0.881, 0.802, 0.928, 0.814], [0.515, 0.815, 0.928, 0.827], [0.515, 0.829, 0.928, 0.841], [0.515, 0.843, 0.572, 0.854]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 110, "edu_l1_label": "IOS"}, {"txt": "We further assume that the orientation of the nanoparticle is controlled.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3400000, "bbox": [[0.531, 0.86, 0.928, 0.871], [0.515, 0.873, 0.646, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 111, "edu_l1_label": "IOS"}, {"txt": "This could be achieved, for instance,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3400000, "bbox": [[0.646, 0.873, 0.928, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 112, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3500000, "bbox": [[0.917, 0.088, 0.932, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 113, "edu_l1_label": "EDU_O"}, {"txt": "if the particle exhibits an electric dipole moment and is subjected to a homogeneous electric feld;", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3500000, "bbox": [[0.071, 0.121, 0.485, 0.133], [0.071, 0.134, 0.381, 0.146]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 114, "edu_l1_label": "IOS"}, {"txt": " nanoscale rotational control schemes have been proposed and tested recently [52–54].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3500000, "bbox": [[0.381, 0.134, 0.485, 0.146], [0.071, 0.148, 0.485, 0.16], [0.071, 0.162, 0.19, 0.173]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 115, "edu_l1_label": "IOS"}, {"txt": "If the orientation of the nanoparticle isnot controlled, our scheme still works, albeit with a reduced scattering rate into the chosen Bragg peaks and a loss of contrast due to imperfect Bragg peak selection.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3500000, "bbox": [[0.19, 0.162, 0.485, 0.173], [0.071, 0.175, 0.485, 0.187], [0.071, 0.189, 0.485, 0.201], [0.071, 0.202, 0.469, 0.214]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 116, "edu_l1_label": "IOS"}, {"txt": "Localized charges attached to the nanoparticle (e.g., remaining surface charges or charges created by the electron beam) will induce an additional electrostatic defection of the electrons by an angle of the order of e2/(2πε0meγv2d), where γ = (1 −v2/c2)−1/2 is theLorentz factor, c is the speed of light and d is the impact parameter of the electron with respect to the localized charge.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3600000, "bbox": [[0.088, 0.216, 0.485, 0.228], [0.071, 0.23, 0.485, 0.242], [0.071, 0.244, 0.485, 0.255], [0.071, 0.257, 0.485, 0.269], [0.071, 0.271, 0.485, 0.283], [0.071, 0.284, 0.485, 0.296], [0.071, 0.298, 0.485, 0.31], [0.071, 0.312, 0.123, 0.323]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 117, "edu_l1_label": "IOS"}, {"txt": "For d = 1 nm and a kinetic energy of 300 keV, the defection angle is of the order of 10−5 rad and can besafely neglected.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3600000, "bbox": [[0.123, 0.312, 0.485, 0.323], [0.071, 0.325, 0.485, 0.337], [0.071, 0.339, 0.19, 0.351]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 118, "edu_l1_label": "IOS"}, {"txt": "Another potential risk for the experiment could be the electron-induced sublimation of silicon atoms, changing the mass and potentially the shape of the nanoparticle.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3700000, "bbox": [[0.088, 0.353, 0.485, 0.364], [0.071, 0.366, 0.485, 0.378], [0.071, 0.38, 0.485, 0.392]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 119, "edu_l1_label": "IOS"}, {"txt": "However, due to the relatively low electron dose proposed for the successful implementation of the experiment (106 electrons per 3.7×104 nm2 cross-section area), the chanceof a sputtering event is negligible [55].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3700000, "bbox": [[0.071, 0.393, 0.485, 0.405], [0.071, 0.407, 0.484, 0.414], [0.071, 0.421, 0.485, 0.432], [0.071, 0.434, 0.346, 0.446]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 120, "edu_l1_label": "IOS"}, {"txt": "Back-scattering of a 300 keV electron would impart at most 0.2 mm/s onto the nanoparticle, which does not lead to particle loss.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3700000, "bbox": [[0.346, 0.434, 0.485, 0.446], [0.071, 0.448, 0.485, 0.46], [0.071, 0.461, 0.463, 0.473]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 121, "edu_l1_label": "IOS"}, {"txt": "Optical trapping of nanoparticles can result in high internal temperatures due to photon absorption [56], which may cause a gradual rearranging of atoms in the crystal and thus deformation.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3800000, "bbox": [[0.088, 0.475, 0.485, 0.487], [0.071, 0.489, 0.485, 0.501], [0.071, 0.503, 0.485, 0.514], [0.071, 0.516, 0.234, 0.528]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 122, "edu_l1_label": "IOS"}, {"txt": "This problem could be mitigated by employing a suitable dielectric material with low absorption or by operating with a charged nanoparticle in an ion trap [19, 20].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3800000, "bbox": [[0.234, 0.516, 0.485, 0.528], [0.071, 0.53, 0.485, 0.542], [0.071, 0.543, 0.485, 0.555], [0.071, 0.557, 0.216, 0.569]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 123, "edu_l1_label": "IOS"}, {"txt": "IV.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3900000, "bbox": [[0.131, 0.599, 0.157, 0.609]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 12, "global_sentence_id": 124, "edu_l1_label": "BOS"}, {"txt": "DECOHERENCE ESTIMATES", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 3900000, "bbox": [[0.174, 0.599, 0.425, 0.609]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 12, "global_sentence_id": 125, "edu_l1_label": "IOS"}, {"txt": "Massive neutral particles are subject to decoherence, mainly caused by emission of thermal radiation and by collisions with residual gas particles [57].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.088, 0.628, 0.485, 0.64], [0.071, 0.642, 0.485, 0.654], [0.071, 0.656, 0.365, 0.667]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 126, "edu_l1_label": "IOS"}, {"txt": "The result is an exponential reduction of fringe visibility with an exponent Γdec(t + t0), proportional to the total interference timeand an efective decoherence rate that depends on the material properties, the mass M, and the fringe period d. Compared to other high-mass interference schemes, the interference time and fringe period are much shorter here, alleviating the impact of decoherence.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.365, 0.656, 0.485, 0.667], [0.071, 0.669, 0.485, 0.681], [0.071, 0.683, 0.485, 0.695], [0.071, 0.696, 0.485, 0.708], [0.071, 0.71, 0.485, 0.722], [0.071, 0.724, 0.485, 0.735], [0.071, 0.737, 0.485, 0.749], [0.071, 0.751, 0.349, 0.763]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 127, "edu_l1_label": "IOS"}, {"txt": "For a simple conservative estimate, we extrapolate from the experiment proposed in Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.349, 0.751, 0.485, 0.763], [0.071, 0.764, 0.485, 0.776], [0.071, 0.778, 0.197, 0.79]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 128, "edu_l1_label": "IOS"}, {"txt": "[25] for a silicon particle of 106 amu, with 102 ms interference time, and 103 nm fringe period.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.197, 0.778, 0.485, 0.79], [0.071, 0.792, 0.485, 0.803]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 129, "edu_l1_label": "IOS"}, {"txt": "Here, the mass is more than a factor 103 greater, the interference time 103 smaller, and the fringe period more than 103 smaller.For the case of gas collisions, Γdecis conservatively estimated by the collision rate, which scales roughly like M 2/5.Decoherence is therefore reduced by about 10−9/5 compared to Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.071, 0.805, 0.485, 0.817], [0.071, 0.819, 0.485, 0.831], [0.071, 0.832, 0.484, 0.845], [0.071, 0.846, 0.485, 0.858], [0.071, 0.86, 0.485, 0.871], [0.071, 0.873, 0.373, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 130, "edu_l1_label": "IOS"}, {"txt": "[25].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.373, 0.873, 0.41, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 131, "edu_l1_label": "IOS"}, {"txt": "Decoher-", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.41, 0.873, 0.485, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 132, "edu_l1_label": "IOS"}, {"txt": "ence by thermal emission can be modeled as a difusion process due to the weak recoil of blackbody photons at µm-sized wavelengths.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.515, 0.121, 0.928, 0.133], [0.515, 0.134, 0.928, 0.146], [0.515, 0.148, 0.678, 0.16]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 133, "edu_l1_label": "IOS"}, {"txt": "In this case, Γdec ∝Md2, whichyields a decoherence efect suppressed by 10−6 relativeto Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.678, 0.148, 0.928, 0.16], [0.515, 0.162, 0.928, 0.173], [0.515, 0.175, 0.565, 0.187]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 134, "edu_l1_label": "IOS"}, {"txt": "[25].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.565, 0.175, 0.601, 0.187]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 135, "edu_l1_label": "IOS"}, {"txt": "Hence, decoherence should be irrelevant for vacuum pressures of 10−9 mbar, which is achievable inmodern TEMs [58], and internal particle temperatures below their melting point.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4000000, "bbox": [[0.601, 0.175, 0.928, 0.187], [0.515, 0.189, 0.928, 0.201], [0.515, 0.202, 0.928, 0.214], [0.515, 0.216, 0.705, 0.228]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 136, "edu_l1_label": "IOS"}, {"txt": "Dephasing due to charging of the nanoparticle can also be safely neglected.The dipole trap is placed in between the pole pieces of the TEM, providing a spherical volume with a radius r = 2 mm of vacuum to decouple the nanoparticle from the environment.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4100000, "bbox": [[0.531, 0.23, 0.928, 0.242], 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DISCUSSION", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4200000, "bbox": [[0.648, 0.393, 0.666, 0.403], [0.684, 0.393, 0.795, 0.403]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 10, "global_sentence_id": 139, "edu_l1_label": "BOS"}, {"txt": "The proposed electron-enabled nanoparticle difraction scheme represents a viable route towards high-mass matter-wave experiments with levitated nanoparticles at the mass scale of 109 amu and beyond.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4300000, "bbox": [[0.531, 0.422, 0.928, 0.434], [0.515, 0.436, 0.928, 0.448], [0.515, 0.449, 0.928, 0.461], [0.515, 0.463, 0.806, 0.475]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 140, "edu_l1_label": "IOS"}, {"txt": "Leveraging the precise control and high spatio-temporal resolution of present-day transmission electron microscopy, the END scheme exploits the coherent recoil caused by Bragg difraction of atomic structures, which entangles the wavefunctions of electron and nanoparticle.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4300000, "bbox": [[0.806, 0.463, 0.928, 0.475], [0.515, 0.477, 0.928, 0.488], [0.515, 0.49, 0.928, 0.502], [0.515, 0.504, 0.928, 0.516], [0.515, 0.517, 0.928, 0.529], [0.515, 0.531, 0.837, 0.543]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 141, "edu_l1_label": "IOS"}, {"txt": "Upon electron detection, the particle self-interferes within a short free-fall time of less than a millisecond (at 109 amu); see Table I.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4300000, "bbox": [[0.837, 0.531, 0.928, 0.543], [0.515, 0.545, 0.928, 0.556], [0.515, 0.558, 0.928, 0.57], [0.515, 0.572, 0.609, 0.584]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 142, "edu_l1_label": "IOS"}, {"txt": "This not only relaxes the experimental constraints associated with high-vacuum conditions and black-body radiation, but it also facilitates a reliable recapture of the nanoparticles and fast experimental duty cycles.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4300000, "bbox": [[0.609, 0.572, 0.928, 0.584], [0.515, 0.585, 0.928, 0.597], [0.515, 0.599, 0.928, 0.611], [0.515, 0.613, 0.928, 0.625], [0.515, 0.626, 0.562, 0.638]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 143, "edu_l1_label": "IOS"}, {"txt": "Our exemplary case study with M = 2 × 109 amu andan interference time t = 1 ms could reach a logarithmic macroscopicity as high as µ ≈16.3—two orders of mag-nitude above the status quo [10, 59].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4400000, "bbox": [[0.531, 0.64, 0.928, 0.652], [0.515, 0.654, 0.928, 0.665], [0.515, 0.667, 0.928, 0.679], [0.515, 0.681, 0.792, 0.693]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 144, "edu_l1_label": "IOS"}, {"txt": "This is based on an empirical measure that compares the ‘size’ of quan-tum superposition states achieved in experiments with mechanical degrees of freedom [60]; see App.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4400000, "bbox": [[0.792, 0.681, 0.928, 0.693], [0.515, 0.694, 0.928, 0.706], [0.515, 0.708, 0.928, 0.72], [0.515, 0.722, 0.852, 0.733]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 145, "edu_l1_label": "IOS"}, {"txt": "C for details.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4400000, "bbox": [[0.852, 0.722, 0.928, 0.733], [0.515, 0.735, 0.55, 0.747]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 146, "edu_l1_label": "IOS"}, {"txt": "Going further, one could envisage whole sequences of consecutive electron interactions for multi-particle entanglement and interference experiments within shallow nanoparticle traps.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4400000, "bbox": [[0.55, 0.735, 0.928, 0.747], [0.515, 0.749, 0.928, 0.761], [0.515, 0.762, 0.928, 0.774], [0.515, 0.776, 0.652, 0.788]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 147, "edu_l1_label": "IOS"}, {"txt": "ACKNOWLEDGEMENTS", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4500000, "bbox": [[0.616, 0.816, 0.827, 0.827]]}]}, "tags": ["title"], "label": "title1", "web_segment_id": 11, "global_sentence_id": 148, "edu_l1_label": "IOS"}, {"txt": "The authors thank Markus Arndt, Peter Schattschneider and Paul Hamilton for fruitful discussions.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4600000, "bbox": [[0.531, 0.846, 0.928, 0.858], [0.515, 0.86, 0.845, 0.871]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 9, "global_sentence_id": 149, "edu_l1_label": "IOS"}, {"txt": "PH thanks the Austrian Science Fund (FWF): Y1121, P36041,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4600000, "bbox": [[0.845, 0.86, 0.928, 0.871], [0.515, 0.873, 0.727, 0.885], [0.727, 0.873, 0.928, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 9, "global_sentence_id": 150, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4700000, "bbox": [[0.917, 0.089, 0.932, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 151, "edu_l1_label": "EDU_O"}, {"txt": "P35953 and the FFG-project AQUTEM.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4700000, "bbox": [[0.071, 0.121, 0.38, 0.133]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 152, "edu_l1_label": "IOS"}, {"txt": "DR acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’sExcellence Strategy – EXC-2123 QuantumFrontiers390837967.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4700000, "bbox": [[0.38, 0.121, 0.485, 0.133], [0.071, 0.134, 0.485, 0.146], [0.071, 0.148, 0.485, 0.16], [0.071, 0.162, 0.466, 0.173], [0.071, 0.175, 0.151, 0.187]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 153, "edu_l1_label": "IOS"}, {"txt": "Appendix A:", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4700000, "bbox": [[0.1, 0.217, 0.2, 0.228]]}]}, "tags": ["title"], "label": "content", "web_segment_id": 9, "global_sentence_id": 154, "edu_l1_label": "EDU_O"}, {"txt": " Efective grating transformation", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4700000, "bbox": [[0.2, 0.217, 0.456, 0.228]]}]}, "tags": ["title"], "label": "content", "web_segment_id": 9, "global_sentence_id": 155, "edu_l1_label": "EDU_O"}, {"txt": "Consider the Bragg difraction of a pulsed singleelectron beam at a single silicon crystal, determined by a scattering operator Sˆ = 1 + i Tˆ that maps an incom-ing wave function |ψin⟩into |ψout⟩= |ψin⟩+ i Tˆ|ψin⟩.We operate in the paraxial regime of high kinetic energy (E0 = eU), in which the de Broglie wavelength, λ = hc/E0(2mec2 + E0), is much smaller than the lat-tice consptant a.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4800000, "bbox": [[0.088, 0.247, 0.485, 0.259], [0.071, 0.261, 0.485, 0.273], [0.071, 0.274, 0.485, 0.286], [0.071, 0.288, 0.337, 0.308], [0.347, 0.288, 0.485, 0.3], [0.071, 0.302, 0.485, 0.313], [0.071, 0.315, 0.485, 0.327], [0.071, 0.33, 0.485, 0.342], [0.071, 0.344, 0.183, 0.356]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 156, "edu_l1_label": "IOS"}, {"txt": "Then, given beam propagation along the z-axis and a not too large crystal volume, the electron will undergo a single small-angle scattering transformation at the crystal’s periodic lattice of atoms, as described by theeikonal approximation [38],", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4800000, "bbox": [[0.183, 0.344, 0.485, 0.356], [0.071, 0.358, 0.485, 0.37], [0.071, 0.371, 0.485, 0.383], [0.071, 0.385, 0.485, 0.397], [0.071, 0.399, 0.27, 0.41]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 157, "edu_l1_label": "EDU_O"}, {"txt": "s≈exp", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4900000, "bbox": [[0.15, 0.432, 0.211, 0.45]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 35, "global_sentence_id": 158, "edu_l1_label": "IOS"}, {"txt": "心", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4900000, "bbox": [[0.225, 0.434, 0.246, 0.446]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 34, "global_sentence_id": 159, "edu_l1_label": "IOS"}, {"txt": "p(r", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4900000, "bbox": [[0.346, 0.438, 0.369, 0.446]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 33, "global_sentence_id": 160, "edu_l1_label": "IOS"}, {"txt": "(A1)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4900000, "bbox": [[0.451, 0.436, 0.485, 0.448]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 15, "global_sentence_id": 161, "edu_l1_label": "IOS"}, {"txt": "hkl", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 4900000, "bbox": [[0.224, 0.45, 0.254, 0.462]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 32, "global_sentence_id": 162, "edu_l1_label": "IOS"}, {"txt": "Here, ˆr⊥= (xˆ, yˆ) denotes the transverse position opera-tor of the electron relative to the crystal’s centre of mass.The sum consists of Bragg momentum displacements by reciprocal lattice vectors ghkℓof length ghkℓ= 2π/dhkℓ,specifed by Miller indices (hkℓ).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5000000, "bbox": [[0.071, 0.474, 0.485, 0.486], [0.071, 0.487, 0.485, 0.499], [0.071, 0.501, 0.485, 0.513], [0.071, 0.515, 0.485, 0.527], [0.071, 0.528, 0.311, 0.54]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 163, "edu_l1_label": "IOS"}, {"txt": "The displacements areweighted by the amplitudes", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5000000, "bbox": [[0.311, 0.528, 0.485, 0.54], [0.071, 0.542, 0.273, 0.554]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 164, "edu_l1_label": "EDU_O"}, {"txt": "Jnke = Fhke", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.102, 0.578, 0.189, 0.593]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 28, "global_sentence_id": 165, "edu_l1_label": "IOS"}, {"txt": "1+", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.201, 0.581, 0.223, 0.589]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 27, "global_sentence_id": 166, "edu_l1_label": "IOS"}, {"txt": "EO", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.239, 0.571, 0.261, 0.582]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 30, "global_sentence_id": 167, "edu_l1_label": "IOS"}, {"txt": "2Z", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.314, 0.571, 0.335, 0.582]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 29, "global_sentence_id": 168, "edu_l1_label": "IOS"}, {"txt": "zg(3sià", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.323, 0.562, 0.39, 0.588]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 31, "global_sentence_id": 169, "edu_l1_label": "IOS"}, {"txt": "(A2)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.451, 0.578, 0.485, 0.59]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 14, "global_sentence_id": 170, "edu_l1_label": "IOS"}, {"txt": "mec2/1 + (2πasi/dhkt)2 ′", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5100000, "bbox": [[0.226, 0.58, 0.425, 0.604]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 26, "global_sentence_id": 171, "edu_l1_label": "IOS"}, {"txt": "assuming single-atom scattering in the Wentzel model at small scattering angles, with atomic parameters ZSi = 14, aSi = a0/ZS1i/ 3, and a0 the Bohr radius.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5200000, "bbox": [[0.071, 0.612, 0.485, 0.623], [0.071, 0.625, 0.485, 0.637], [0.071, 0.641, 0.365, 0.653]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 172, "edu_l1_label": "IOS"}, {"txt": "The term Fhkℓis the structure factor of the lattice unit cell.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5200000, "bbox": [[0.365, 0.641, 0.484, 0.654], [0.071, 0.655, 0.402, 0.666]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 173, "edu_l1_label": "IOS"}, {"txt": "Of course, the Bragg difraction in (A1) is restricted to beam trajectories that penetrate the crystal volume V ≫a3, whichis taken into account by the homogeneous, trajectoryaveraged density of unit cells ϱ(r⊥) =dz ϱ(r⊥+ zez).For an oblate ellipsoid of thickness 2bMR and radius RM containing Ncell unit cells, we get", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5200000, "bbox": [[0.402, 0.655, 0.485, 0.666], [0.071, 0.668, 0.485, 0.68], [0.071, 0.682, 0.485, 0.694], [0.071, 0.695, 0.485, 0.707], [0.071, 0.709, 0.485, 0.721], [0.071, 0.723, 0.483, 0.735], [0.071, 0.736, 0.315, 0.748]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 174, "edu_l1_label": "IOS"}, {"txt": "@(r⊥) =", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.114, 0.77, 0.176, 0.784]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 22, "global_sentence_id": 175, "edu_l1_label": "IOS"}, {"txt": "Ncell", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.18, 0.761, 0.216, 0.776]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 24, "global_sentence_id": 176, "edu_l1_label": "IOS"}, {"txt": "V", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.192, 0.778, 0.206, 0.788]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 20, "global_sentence_id": 177, "edu_l1_label": "IOS"}, {"txt": "d≥0", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.237, 0.77, 0.276, 0.781]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 23, "global_sentence_id": 178, "edu_l1_label": "IOS"}, {"txt": "r2", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.322, 0.761, 0.347, 0.773]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 25, "global_sentence_id": 179, "edu_l1_label": "IOS"}, {"txt": "RM", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.316, 0.773, 0.35, 0.791]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 41, "global_sentence_id": 180, "edu_l1_label": "IOS"}, {"txt": "6M", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.358, 0.773, 0.405, 0.794]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 21, "global_sentence_id": 181, "edu_l1_label": "IOS"}, {"txt": "(A3)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5300000, "bbox": [[0.451, 0.77, 0.485, 0.782]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 17, "global_sentence_id": 182, "edu_l1_label": "IOS"}, {"txt": "with Θ the Heaviside function and V = 4πbMRM2/3.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5400000, "bbox": [[0.071, 0.805, 0.455, 0.817]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 10, "global_sentence_id": 183, "edu_l1_label": "IOS"}, {"txt": "Silicon has a diamond cubic crystal structure with lattice constant a = 543 pm, a primitive unit cell of 2 atoms, and a structure factor Fhkℓ= 2 cos[(h + k + ℓ)π/4];", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5500000, "bbox": [[0.088, 0.819, 0.485, 0.831], [0.071, 0.832, 0.485, 0.844], [0.071, 0.846, 0.452, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 184, "edu_l1_label": "IOS"}, {"txt": " anyBragg order for which (h + k + ℓ)/2 is an odd integer istherefore kinematically forbidden.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5500000, "bbox": [[0.452, 0.846, 0.485, 0.858], [0.071, 0.86, 0.485, 0.871], [0.071, 0.873, 0.319, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 185, "edu_l1_label": "EDU_O"}, {"txt": "As the electron propagates freely to the far-feld, or back focal plane of an objective lens, its wavefunction separates into spatially distinct Bragg components.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5600000, "bbox": [[0.531, 0.121, 0.928, 0.133], [0.515, 0.134, 0.928, 0.146], [0.515, 0.148, 0.901, 0.16]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 186, "edu_l1_label": "IOS"}, {"txt": "A transmission mask of circular pinholes allows us to select a subset of these components and block all the others.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5600000, "bbox": [[0.915, 0.148, 0.928, 0.16], [0.515, 0.162, 0.928, 0.173], [0.515, 0.175, 0.928, 0.187]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 187, "edu_l1_label": "IOS"}, {"txt": "We can describe this by multiplying an aperture function M(p⊥) to the state in momentum representation,|ψout⟩→|ψsel⟩= M(pˆ⊥)|ψout⟩.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5600000, "bbox": [[0.515, 0.189, 0.928, 0.201], [0.515, 0.202, 0.928, 0.214], [0.515, 0.216, 0.748, 0.228]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 188, "edu_l1_label": "IOS"}, {"txt": "Here we consider a lin-ear confguration of pinholes separated along the spacefxed x-axis by multiples of a fxed difraction momentum 2πℏ/d,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5600000, "bbox": [[0.748, 0.216, 0.928, 0.228], [0.515, 0.23, 0.928, 0.241], [0.515, 0.243, 0.928, 0.255], [0.515, 0.257, 0.564, 0.269]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 189, "edu_l1_label": "IOS"}, {"txt": "M(p⊥) =", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.584, 0.286, 0.713, 0.303]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 39, "global_sentence_id": 190, "edu_l1_label": "IOS"}, {"txt": "n≠0", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.658, 0.303, 0.686, 0.318]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 36, "global_sentence_id": 191, "edu_l1_label": "IOS"}, {"txt": "2πh", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.784, 0.279, 0.815, 0.295]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 40, "global_sentence_id": 192, "edu_l1_label": "IOS"}, {"txt": "DI", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.735, 0.293, 0.754, 0.299]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 38, "global_sentence_id": 193, "edu_l1_label": "IOS"}, {"txt": "d", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.787, 0.295, 0.807, 0.307]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 37, "global_sentence_id": 194, "edu_l1_label": "IOS"}, {"txt": "(A4)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5700000, "bbox": [[0.894, 0.288, 0.928, 0.3]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 16, "global_sentence_id": 195, "edu_l1_label": "IOS"}, {"txt": "where we choose a d = dh0k0ℓ0 with a sizeable scatteringamplitude fh0k0ℓ0.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5800000, "bbox": [[0.515, 0.325, 0.928, 0.337], [0.515, 0.339, 0.647, 0.351]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 196, "edu_l1_label": "IOS"}, {"txt": "Each pinhole thus selects a difractioncomponent of the scattered electron state with matching Bragg momentum, ghkℓ= 2πn/d, provided there is onepointing in x-direction for the given crystal orientation.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5800000, "bbox": [[0.647, 0.339, 0.928, 0.351], [0.515, 0.352, 0.928, 0.364], [0.515, 0.366, 0.928, 0.378], [0.515, 0.38, 0.928, 0.391]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 197, "edu_l1_label": "IOS"}, {"txt": "Since we assume that the undifracted component (n = 0) is blocked, M(pˆ⊥)|ψin⟩= 0, the overall transformationcan be written as |ψsel⟩= iM(pˆ⊥) Tˆ|ψin⟩.Expandingthe scattering operator (A1) to linear order, we can further simplify Tˆ ≈hstudy, we pick (h0kP0ℓ0) from the {1¯10}-⊥family of latticeplanes with a fairly large period, d = a/2√2 = 192 pm,and we transmit the Bragg peaks up to the second order, n = ±1, ±2.Expressed in terms of the conven-tional cubic unit cell, the chosen family corresponds to {H0K0L0} = {20¯2} [61].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5800000, "bbox": [[0.515, 0.393, 0.928, 0.405], [0.515, 0.407, 0.928, 0.419], [0.515, 0.422, 0.928, 0.434], [0.515, 0.436, 0.928, 0.448], [0.515, 0.451, 0.676, 0.466], [0.515, 0.465, 0.928, 0.477], [0.515, 0.48, 0.928, 0.491], [0.515, 0.493, 0.928, 0.505], [0.515, 0.507, 0.928, 0.519], [0.515, 0.52, 0.928, 0.532], [0.515, 0.534, 0.694, 0.546]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 198, "edu_l1_label": "IOS"}, {"txt": "The electron then propagates further (either freely or by means of lens imaging) to the image plane where the selected Bragg orders interfere and form a fringe pattern of period d. Measuring the electron in a positionresolving detector amounts to projecting the wavefunction |ψsel⟩onto a position eigenstate |r⊥⟩correspondingto the registered outcome.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5900000, "bbox": [[0.531, 0.548, 0.928, 0.56], [0.515, 0.561, 0.928, 0.573], [0.515, 0.575, 0.928, 0.587], [0.515, 0.588, 0.928, 0.6], [0.515, 0.602, 0.928, 0.614], [0.515, 0.616, 0.928, 0.628], [0.515, 0.629, 0.709, 0.641]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 199, "edu_l1_label": "IOS"}, {"txt": "This assumes a spatial resolution much better than d.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 5900000, "bbox": [[0.709, 0.629, 0.928, 0.641], [0.515, 0.643, 0.71, 0.655]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 200, "edu_l1_label": "IOS"}, {"txt": "So far, we have treated the crystal as a fxed motionless object.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6000000, "bbox": [[0.531, 0.657, 0.928, 0.668], [0.515, 0.67, 0.597, 0.682]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 201, "edu_l1_label": "IOS"}, {"txt": "In our setting however, both the centre-ofmass position R and the orientation Ωof the crystal aredynamical (quantum) variables that enter the scattering transformation Tˆ.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6000000, "bbox": [[0.597, 0.67, 0.928, 0.682], [0.515, 0.684, 0.928, 0.696], [0.515, 0.697, 0.928, 0.709], [0.515, 0.713, 0.647, 0.725]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 202, "edu_l1_label": "IOS"}, {"txt": "We can re-introduce them explicitlyby noting that the electron position in Tˆ is measuredrelative to R⊥= (X, Y ) and the body-fxed reciprocallattice vectors ghkℓare rotated by Ωwith respect to thespace-fxed frame,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6000000, "bbox": [[0.647, 0.713, 0.928, 0.725], [0.515, 0.726, 0.928, 0.738], [0.515, 0.74, 0.928, 0.752], [0.515, 0.754, 0.928, 0.765], [0.515, 0.767, 0.646, 0.779]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 203, "edu_l1_label": "IOS"}, {"txt": "T(R⊥,A) = fhk(e′R(0)9ne(t⊥-R⊥)w(f⊥ = R⊥).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6100000, "bbox": [[0.533, 0.788, 0.91, 0.808]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 19, "global_sentence_id": 204, "edu_l1_label": "IOS"}, {"txt": "hkl", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6100000, "bbox": [[0.629, 0.808, 0.651, 0.82]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 18, "global_sentence_id": 205, "edu_l1_label": "IOS"}, {"txt": "(A5)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6100000, "bbox": [[0.894, 0.819, 0.928, 0.831]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 12, "global_sentence_id": 206, "edu_l1_label": "IOS"}, {"txt": "Here, R(Ω) denotes a rotation matrix, which one canparametrise in terms of Euler angles (αβγ), for example.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6200000, "bbox": [[0.515, 0.832, 0.928, 0.844], [0.515, 0.846, 0.928, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 13, "global_sentence_id": 207, "edu_l1_label": "IOS"}, {"txt": "Now let |Ψcm⟩be the centre-of-mass wavefunction ofthe nanoparticle upon the scattering event and let |Ω⟩be", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6300000, "bbox": [[0.531, 0.86, 0.928, 0.871], [0.515, 0.873, 0.928, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 11, "global_sentence_id": 208, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6400000, "bbox": [[0.916, 0.088, 0.932, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 209, "edu_l1_label": "EDU_O"}, {"txt": "an arbitrary orientation state of the lattice.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6400000, "bbox": [[0.071, 0.121, 0.388, 0.133]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 210, "edu_l1_label": "IOS"}, {"txt": "The scattering operator Tˆ acts on the product state of electron andcrystal.Conditioned on the detected electron position r⊥, the Bragg scattering event transforms the motionalstate of the crystal as |Ψcm⟩|Ω⟩→Kˆ(r⊥, Ω)|Ψcm⟩|Ω⟩,where", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6400000, "bbox": [[0.388, 0.121, 0.485, 0.133], [0.071, 0.134, 0.485, 0.146], [0.071, 0.148, 0.485, 0.16], [0.071, 0.162, 0.485, 0.173], [0.071, 0.175, 0.485, 0.187], [0.071, 0.189, 0.114, 0.201]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 211, "edu_l1_label": "IOS"}, {"txt": "K(r⊥,Ω) = (r⊥|iM(p⊥)f(R⊥,N)|vin).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6500000, "bbox": [[0.114, 0.212, 0.408, 0.231]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 29, "global_sentence_id": 212, "edu_l1_label": "IOS"}, {"txt": "(A6)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6500000, "bbox": [[0.451, 0.217, 0.485, 0.228]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 10, "global_sentence_id": 213, "edu_l1_label": "IOS"}, {"txt": "Here we neglect the electron’s time of fight to the de-tector, which is much shorter than any motional time scale of the crystal.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6600000, "bbox": [[0.071, 0.244, 0.485, 0.256], [0.071, 0.258, 0.485, 0.27], [0.071, 0.272, 0.216, 0.283]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 214, "edu_l1_label": "IOS"}, {"txt": "The transformation of the reduced centre-of-mass state is then obtained by averaging over a distribution µ(Ω) of orientations the crystal assumes atthe moment of scattering, given an uncorrelated incoherent mixture of orientations.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6600000, "bbox": [[0.216, 0.272, 0.485, 0.283], [0.071, 0.285, 0.485, 0.297], [0.071, 0.299, 0.485, 0.311], [0.071, 0.312, 0.485, 0.324], [0.071, 0.326, 0.268, 0.338]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 215, "edu_l1_label": "IOS"}, {"txt": "For a general (pure or mixed) state ρcm, the transformation reads as", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6600000, "bbox": [[0.268, 0.326, 0.485, 0.338], [0.071, 0.34, 0.351, 0.351]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 216, "edu_l1_label": "IOS"}, {"txt": "d3Ωμμ(Ω)K(r⊥,Ω)pcmRt(r⊥,Ω),", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6700000, "bbox": [[0.172, 0.368, 0.421, 0.387]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 28, "global_sentence_id": 217, "edu_l1_label": "IOS"}, {"txt": "(A7)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6700000, "bbox": [[0.451, 0.373, 0.485, 0.385]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 12, "global_sentence_id": 218, "edu_l1_label": "IOS"}, {"txt": "which can be seen as the Kraus representation of a completely positive (but not trace-preserving) map on the centre-of-mass state.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6800000, "bbox": [[0.071, 0.407, 0.485, 0.419], [0.071, 0.421, 0.485, 0.433], [0.071, 0.434, 0.223, 0.446]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 219, "edu_l1_label": "IOS"}, {"txt": "We will see that it acts as a partially coherent grating transformation that can lead to de Broglie self-interference of the crystal, depending on the spread of orientations averaged over.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6800000, "bbox": [[0.223, 0.434, 0.485, 0.446], [0.071, 0.448, 0.485, 0.46], [0.071, 0.462, 0.485, 0.473], [0.071, 0.475, 0.339, 0.487]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 220, "edu_l1_label": "IOS"}, {"txt": "Let us frst summarize the transformation of the elec tron beam that defnes the overall map (A7).Given a crystal position R⊥, the function K(r⊥, Ω) in (A6)describes the amplitude of the electron wavefunction at r⊥on the detection plane.To arrive there, the incoming wavefunction undergoes three transformation steps.First, it is multiplied by the averaged homogeneous density ϱ describing the cross-section area withinwhich the electron enters the crystal and Bragg scattering can take place.This efective aperture smears out the momentum spread of the initial electron wavefunction, which we give in units of wavenumbers by the standard deviation ∆kin.Concretely, the Fouriertransform of (A3) for an oblate spheroidal crystal volume, ϱ˜(k⊥) = 3Ncellj1(k⊥RM)/k⊥RM with j1 a spheri-cal Bessel function, contributes a spread of the order of ∆kvol ≈4.5/RM, as per the frst zero of j1(x)/x.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 6900000, "bbox": [[0.088, 0.49, 0.479, 0.502], [0.071, 0.504, 0.485, 0.515], [0.071, 0.517, 0.485, 0.529], [0.071, 0.531, 0.485, 0.543], [0.071, 0.544, 0.307, 0.556], [0.328, 0.544, 0.485, 0.556], [0.071, 0.558, 0.485, 0.57], [0.071, 0.572, 0.485, 0.583], [0.071, 0.585, 0.485, 0.597], [0.071, 0.599, 0.485, 0.611], [0.071, 0.612, 0.485, 0.624], [0.071, 0.626, 0.485, 0.638], [0.071, 0.64, 0.485, 0.651], [0.071, 0.653, 0.485, 0.665], [0.071, 0.667, 0.485, 0.679], [0.071, 0.68, 0.485, 0.692], [0.071, 0.694, 0.485, 0.706], [0.071, 0.708, 0.429, 0.719]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 221, "edu_l1_label": "IOS"}, {"txt": "Secondly, the smeared wavefunction undergoes Bragg difraction at the crystal lattice, which splits it into a weighted superposition of momentum-displaced instances, as seen in (A5).Since the Bragg momenta are much larger than the incoming wavefunction spread, ghkℓ≫∆kin, ∆kvol, the displaced wavefunctions do notoverlap with one another.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7000000, "bbox": [[0.088, 0.722, 0.485, 0.734], [0.071, 0.736, 0.485, 0.748], [0.071, 0.75, 0.485, 0.761], [0.071, 0.763, 0.485, 0.775], [0.071, 0.777, 0.485, 0.789], [0.071, 0.79, 0.485, 0.802], [0.071, 0.804, 0.259, 0.816]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 222, "edu_l1_label": "IOS"}, {"txt": "Thirdly, the transmission mask (A4) blocks the undifracted wavefunction as well as any Bragg-difracted one that does not overlap with one of the pinholes in momentum space, labeled by n. Only those Bragg orders can pass for which [R(Ω)ghkℓ]⊥≈(2πn/d)ex", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7100000, "bbox": [[0.088, 0.819, 0.485, 0.831], [0.071, 0.832, 0.485, 0.844], [0.071, 0.846, 0.485, 0.858], [0.071, 0.86, 0.485, 0.871], [0.071, 0.873, 0.398, 0.886]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 223, "edu_l1_label": "IOS"}, {"txt": "In what follows, we will make four simplifying assumptions in accordance with realistic experimental settings:", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.531, 0.121, 0.928, 0.133], [0.515, 0.134, 0.928, 0.146], [0.515, 0.148, 0.555, 0.16]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 224, "edu_l1_label": "IOS"}, {"txt": " (i) the initial electron wavefunction is Gaussian, ⟨r⊥|ψin⟩∝e−∆ki2nr⊥2, and illuminates a cross-section area greater than the size of the crystal particle, so that ∆kin < ∆kvol.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.555, 0.148, 0.928, 0.16], [0.515, 0.164, 0.605, 0.176], [0.605, 0.162, 0.657, 0.166], [0.661, 0.164, 0.928, 0.176], [0.515, 0.177, 0.928, 0.189], [0.515, 0.191, 0.617, 0.203]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 225, "edu_l1_label": "IOS"}, {"txt": "Next, we assume (ii) that the crystal vol-ume is larger than the spread of its centre-of-mass state, so that we can approximate ϱ(ˆr⊥−R⊥) ≈ϱ(ˆr⊥) in (A5).We introduce the abbreviation |ψin⟩:= ϱ(ˆr⊥)|ψin⟩forthe smeared (and no longer unit-norm) electron wavefunction.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.617, 0.191, 0.928, 0.203], [0.515, 0.205, 0.928, 0.216], [0.515, 0.218, 0.928, 0.23], [0.515, 0.232, 0.928, 0.244], [0.515, 0.245, 0.928, 0.257], [0.515, 0.259, 0.579, 0.271]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 226, "edu_l1_label": "IOS"}, {"txt": "Moreover, (iii) the pinhole apertures M0 shall be large compared to the momentum spread of the smeared electron wavefunction (such that difraction at this aperture is negligible), but small compared to the distance of neighbouring Bragg peaks.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.579, 0.259, 0.928, 0.271], [0.515, 0.273, 0.928, 0.285], [0.515, 0.286, 0.928, 0.298], [0.515, 0.3, 0.928, 0.312], [0.515, 0.314, 0.799, 0.325]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 227, "edu_l1_label": "IOS"}, {"txt": "Mathematically, M0(|pˆ⊥|)|ψin⟩≈|ψin⟩whereas M0(|pˆ⊥−ℏghkℓ|)|ψin⟩≈0for any (hkℓ) = 0.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.799, 0.314, 0.928, 0.325], [0.515, 0.327, 0.928, 0.339], [0.515, 0.341, 0.643, 0.353]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 228, "edu_l1_label": "IOS"}, {"txt": "Finally, (iv) we assume that the crystallattice is brought into a fxed orientation Ω0 upon scat-tering.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.643, 0.341, 0.928, 0.353], [0.515, 0.354, 0.928, 0.366], [0.515, 0.368, 0.562, 0.38]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 229, "edu_l1_label": "IOS"}, {"txt": "In this orientation, the reciprocal lattice vector of the chosen reference Bragg peak (h0k0ℓ0) shall alignwith the x-axis, R(Ω0)gh0k0ℓ0 = (2π/d)ex, such thatthe n-th pinhole of the transmission mask M transmits only the n-th difraction order with relative amplitude fn ≡fnh0,nk0,nℓ0.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7200000, "bbox": [[0.562, 0.368, 0.928, 0.38], [0.515, 0.382, 0.928, 0.393], [0.515, 0.395, 0.928, 0.407], [0.515, 0.409, 0.928, 0.421], [0.515, 0.422, 0.928, 0.434], [0.515, 0.436, 0.641, 0.448]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 230, "edu_l1_label": "IOS"}, {"txt": "Using our assumptions, the conditional transformation (A7) of the centre-of-mass state of the crystal particle reduces to", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7300000, "bbox": [[0.531, 0.45, 0.928, 0.461], [0.515, 0.463, 0.928, 0.475], [0.515, 0.477, 0.589, 0.489]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 231, "edu_l1_label": "IOS"}, {"txt": "Pcm→ K(r⊥,∩0)PcmRt(r⊥,00),", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7400000, "bbox": [[0.596, 0.496, 0.843, 0.516]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 27, "global_sentence_id": 232, "edu_l1_label": "IOS"}, {"txt": "(A8)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7400000, "bbox": [[0.894, 0.523, 0.928, 0.534]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 11, "global_sentence_id": 233, "edu_l1_label": "IOS"}, {"txt": "n≠0", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7400000, "bbox": [[0.718, 0.538, 0.745, 0.55]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 26, "global_sentence_id": 234, "edu_l1_label": "IOS"}, {"txt": "This transformation describes the transmission through a one-dimensional grating aperture of period d [62], shifted by the measured electron position x—the particle is ef-fectively difracted by its own crystal lattice.This is enabled by momentum conservation as each Bragg momentum 2πℏ/d imparted on the electron necessarily im-plies the opposite momentum imparted on the particle, inducing EPR-type entanglement between the wavefunctions of the electron and the particle’s centre of mass [63].The above conditional grating transformation (A8) preserves the purity of the particle wavefunction, but not its norm.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7500000, "bbox": [[0.515, 0.559, 0.928, 0.571], [0.515, 0.573, 0.928, 0.585], [0.515, 0.587, 0.928, 0.599], [0.515, 0.6, 0.928, 0.612], [0.515, 0.614, 0.928, 0.626], [0.515, 0.627, 0.928, 0.639], [0.515, 0.641, 0.928, 0.653], [0.515, 0.655, 0.928, 0.667], [0.515, 0.668, 0.928, 0.68], [0.515, 0.682, 0.928, 0.694], [0.515, 0.696, 0.928, 0.707], [0.515, 0.709, 0.557, 0.721]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 235, "edu_l1_label": "IOS"}, {"txt": "In fact, a successful transformation happens with the probability of an electron arriving anywhere on the detection plane,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7500000, "bbox": [[0.557, 0.709, 0.928, 0.721], [0.515, 0.723, 0.928, 0.735], [0.515, 0.736, 0.631, 0.748]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 236, "edu_l1_label": "IOS"}, {"txt": "Prdet", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7600000, "bbox": [[0.539, 0.765, 0.583, 0.782]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 24, "global_sentence_id": 237, "edu_l1_label": "IOS"}, {"txt": "d2r_tr", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7600000, "bbox": [[0.623, 0.765, 0.676, 0.778]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 25, "global_sentence_id": 238, "edu_l1_label": "IOS"}, {"txt": "pcmK1(r⊥,Q0)K(r⊥,Ωo)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7600000, "bbox": [[0.688, 0.765, 0.879, 0.781]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 23, "global_sentence_id": 239, "edu_l1_label": "IOS"}, {"txt": "~(Win网in)∑Ifn|²", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7600000, "bbox": [[0.583, 0.79, 0.733, 0.808]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 22, "global_sentence_id": 240, "edu_l1_label": "IOS"}, {"txt": "n≠0", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7600000, "bbox": [[0.671, 0.809, 0.698, 0.82]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 21, "global_sentence_id": 241, "edu_l1_label": "IOS"}, 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"label": "content", "web_segment_id": 0, "global_sentence_id": 254, "edu_l1_label": "IOS"}, {"txt": "[25]; we provide a short re-derivation for the present case in App.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.184, 0.175, 0.485, 0.187], [0.071, 0.189, 0.255, 0.201]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 255, "edu_l1_label": "IOS"}, {"txt": "B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.255, 0.189, 0.279, 0.201]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 256, "edu_l1_label": "IOS"}, {"txt": "One starts from a (mixed) Gaussian state of the trapped particle with a small position standard deviation σX ≪d relative to the gratingperiod and a large momentum standard deviation σP ≫2πℏ/d relative to the grating momentum, which corre-sponds to an incoherent point source of matter waves.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.279, 0.189, 0.485, 0.201], [0.071, 0.202, 0.485, 0.214], [0.071, 0.216, 0.485, 0.228], [0.071, 0.23, 0.485, 0.25], [0.071, 0.243, 0.485, 0.255], [0.071, 0.257, 0.485, 0.269]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 257, "edu_l1_label": "IOS"}, {"txt": "Upon release, the particle may evolve freely for the time t0 before the efective grating transformation and for the time t after; coherent dispersion over at least one grating period demands that t0 be of the order of the Talbot time, t0 ≳TM = Md2/2πℏ.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.071, 0.27, 0.485, 0.282], [0.071, 0.284, 0.485, 0.296], [0.071, 0.298, 0.485, 0.31], [0.071, 0.311, 0.485, 0.323], [0.071, 0.325, 0.234, 0.337]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 258, "edu_l1_label": "IOS"}, {"txt": "Assumption (ii) remains valid aslong as σP t0/M ≪RM.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.234, 0.325, 0.485, 0.337], [0.071, 0.339, 0.246, 0.35]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 259, "edu_l1_label": "IOS"}, {"txt": "Finally, one recaptures the par-ticle and measures its position on the X-axis, which one fnds to be distributed according to", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 7900000, "bbox": [[0.246, 0.339, 0.485, 0.35], [0.071, 0.352, 0.485, 0.364], [0.071, 0.366, 0.33, 0.378]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 260, "edu_l1_label": "IOS"}, {"txt": "w3(X) ≈|⟨r⊥|ψin⟩|2 Xe2πin(X/D−x/d)−2π2n2[σXt/d(t+t0)]2n j ×Xfjf j∗+neiπn(2j+n)tt0/TM(t+t0) e−[X+(j+n/2)dt/TM]2/2σ˜X2(A10) √2πσ˜X", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8000000, "bbox": [[0.071, 0.389, 0.486, 0.391], [0.226, 0.405, 0.234, 0.414], [0.166, 0.438, 0.172, 0.446], [0.14, 0.421, 0.385, 0.427], [0.153, 0.454, 0.329, 0.457], [0.442, 0.462, 0.485, 0.474], [0.219, 0.462, 0.272, 0.484]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 17, "global_sentence_id": 261, "edu_l1_label": "IOS"}, {"txt": "given the measured electron position r⊥= (x, y).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8100000, "bbox": [[0.071, 0.491, 0.441, 0.503]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 262, "edu_l1_label": "IOS"}, {"txt": "Thisdensity, normalised toRd2r⊥dX w3(X) ≈Pr det, ex-hibits fringes of a geometrically magnifed period D ≈d(t + t0)/t0 and visibility reduced by the fnite source size σX, inside a broad Gaussian envelope of width σ˜X ≈σP (t + t0)/M.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8100000, "bbox": [[0.441, 0.491, 0.485, 0.503], [0.071, 0.505, 0.485, 0.517], [0.071, 0.518, 0.485, 0.539], [0.071, 0.532, 0.485, 0.544], [0.071, 0.546, 0.485, 0.566], [0.071, 0.559, 0.175, 0.571]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 263, "edu_l1_label": "IOS"}, {"txt": "Notice that the appearance of a fringe pattern in the near feld of a grating does not always certify quantum interference as it could also be explained by a classical shadow efect.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8200000, "bbox": [[0.088, 0.573, 0.485, 0.585], [0.071, 0.586, 0.485, 0.598], [0.071, 0.6, 0.485, 0.612], [0.071, 0.614, 0.174, 0.625]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 264, "edu_l1_label": "IOS"}, {"txt": "Interpreting the initial Gaussian state as the phase-space distribution of a classical particle and treating the grating aperture in (A6) as a classical shadow mask, we obtain the fringe pattern", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8200000, "bbox": [[0.174, 0.614, 0.485, 0.625], [0.071, 0.627, 0.485, 0.639], [0.071, 0.641, 0.485, 0.653], [0.071, 0.654, 0.326, 0.666]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 265, "edu_l1_label": "IOS"}, {"txt": "w3cl (X) ≈|⟨r⊥|ψin⟩|2 Xe2πin(X/D−x/d)−2π2n2[σXt/d(t+t0)]2n ×Xfjf j∗+ne−X2/2σ˜X2√2πσ˜X(A11)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8300000, "bbox": [[0.071, 0.678, 0.245, 0.711], [0.248, 0.678, 0.49, 0.68], [0.229, 0.694, 0.237, 0.702], [0.144, 0.717, 0.236, 0.731], [0.239, 0.709, 0.303, 0.712], [0.246, 0.716, 0.299, 0.739], [0.442, 0.717, 0.485, 0.729]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 12, "global_sentence_id": 266, "edu_l1_label": "IOS"}, {"txt": "The appearance of fringes according to the quantum prediction (A10) does not signify matter-wave coherence whenever they match the classical prediction (A11).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8400000, "bbox": [[0.071, 0.751, 0.485, 0.763], [0.071, 0.764, 0.485, 0.776], [0.071, 0.778, 0.445, 0.79]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 267, "edu_l1_label": "IOS"}, {"txt": "This is for instance the case when t ≪TM.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8400000, "bbox": [[0.445, 0.778, 0.485, 0.79], [0.071, 0.792, 0.355, 0.803]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 268, "edu_l1_label": "IOS"}, {"txt": "In the regime ofa very broad Gaussian envelope, σ˜X ≫dt/TM, it turnsout that the quantum and classical patterns always agree whenever the grating aperture in (A6) comprises only one pair of opposite Bragg orders, say, n = ±1.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8400000, "bbox": [[0.355, 0.792, 0.485, 0.803], [0.071, 0.805, 0.485, 0.817], [0.071, 0.819, 0.485, 0.831], [0.071, 0.832, 0.485, 0.844], [0.071, 0.846, 0.394, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 269, "edu_l1_label": "IOS"}, {"txt": "For a clearquantum signature, one must therefore select at least two Bragg orders of diferent magnitude; see App.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8400000, "bbox": [[0.394, 0.846, 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[[0.695, 0.326, 0.719, 0.335], [0.515, 0.333, 0.861, 0.345]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 281, "edu_l1_label": "EDU_O"}, {"txt": "A.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8700000, "bbox": [[0.861, 0.333, 0.884, 0.345]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 282, "edu_l1_label": "EDU_O"}, {"txt": "Since only the motional state of the particle along the exaxis of the pinhole array matters, we can adopt the onedimensional near-feld interference formalism of Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8700000, "bbox": [[0.884, 0.333, 0.928, 0.345], [0.515, 0.347, 0.928, 0.359], [0.515, 0.36, 0.928, 0.372], [0.515, 0.374, 0.896, 0.386]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 283, "edu_l1_label": "EDU_O"}, {"txt": "[25] and replace the periodic phase grating transformation there by the above transformation.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8700000, "bbox": [[0.896, 0.374, 0.928, 0.386], [0.515, 0.388, 0.928, 0.399], [0.515, 0.401, 0.77, 0.413]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 284, "edu_l1_label": "EDU_O"}, {"txt": "In the phase-space formalism, we represent the onedimensional center-of-mass state in terms of the Wigner function,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8800000, "bbox": [[0.531, 0.415, 0.928, 0.427], [0.515, 0.428, 0.928, 0.44], [0.515, 0.442, 0.579, 0.454]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 285, "edu_l1_label": "IOS"}, {"txt": "w(X, P) = 2πℏdseiP s/ℏX  ρcmX + 2 .", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8900000, "bbox": [[0.531, 0.469, 0.609, 0.481], [0.635, 0.477, 0.662, 0.491], [0.64, 0.461, 0.708, 0.477], [0.722, 0.469, 0.741, 0.489], [0.775, 0.469, 0.804, 0.481], [0.813, 0.469, 0.845, 0.481], [0.85, 0.477, 0.859, 0.489], [0.874, 0.469, 0.878, 0.481]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 18, "global_sentence_id": 286, "edu_l1_label": "IOS"}, {"txt": "(B2)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 8900000, "bbox": [[0.878, 0.469, 0.928, 0.481]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 18, "global_sentence_id": 287, "edu_l1_label": "EDU_O"}, {"txt": "We will assume that the initial state of the nanoparticle upon release is a Gaussian of arbitrary widths σX, σPobeying σXσP ≥ℏ/2.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 9000000, 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j,k", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 9800000, "bbox": [[0.326, 0.134, 0.485, 0.146], [0.071, 0.148, 0.485, 0.16], [0.124, 0.17, 0.141, 0.178]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 312, "edu_l1_label": "IOS"}, {"txt": "One of the key questions for us is whether the observed fringe pattern is non-classical.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 9900000, "bbox": [[0.088, 0.182, 0.485, 0.194], [0.071, 0.196, 0.286, 0.208]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 313, "edu_l1_label": "IOS"}, {"txt": "A direct and setup-specifc way is to compare the interferogram predicted by (B1) to the shadow fringe pattern obtained by treating the efective grating as a classical aperture in phase space.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 9900000, "bbox": [[0.286, 0.196, 0.485, 0.208], [0.071, 0.209, 0.485, 0.221], [0.071, 0.223, 0.485, 0.235], [0.071, 0.237, 0.429, 0.248]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 314, "edu_l1_label": "IOS"}, {"txt": "This is achieved by omitting the argument of the Talbot coefcients (B5) and setting it to zero, so that the transformation kernel (B4) no longer imprints difraction momenta onto the Wigner function and the transformation reduces to the density modulation caused by an efective classical transmission mask with Fourier components Bn(x,y)(0),", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 9900000, "bbox": [[0.429, 0.237, 0.485, 0.248], [0.071, 0.25, 0.485, 0.262], [0.071, 0.264, 0.485, 0.276], [0.071, 0.277, 0.485, 0.289], [0.071, 0.291, 0.485, 0.303], [0.071, 0.305, 0.485, 0.317], [0.071, 0.321, 0.469, 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"label": "content", "web_segment_id": 1, "global_sentence_id": 318, "edu_l1_label": "IOS"}, {"txt": "Conversely, if the quantum interferogram cannot be distinguished from this classical fringe pattern (whether the quantum calculation results in Wigner negativities or not), then one cannot rule out a simple classical model and claim to observe a genuine quantum difraction efect.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10200000, "bbox": [[0.173, 0.418, 0.485, 0.429], [0.071, 0.431, 0.485, 0.443], [0.071, 0.445, 0.485, 0.457], [0.071, 0.458, 0.485, 0.47], [0.071, 0.472, 0.485, 0.484], [0.071, 0.486, 0.115, 0.497]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 319, "edu_l1_label": "IOS"}, {"txt": "We employ this criterion for the interferograms we evaluate here.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10200000, "bbox": [[0.115, 0.486, 0.485, 0.497], [0.071, 0.499, 0.172, 0.511]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 320, "edu_l1_label": "IOS"}, {"txt": "For the Wigner function right after the grating transformation, we frst propagate the initial state (B3) freely by the time t0 and then apply the grating transformation (B4),", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10300000, "bbox": [[0.531, 0.121, 0.928, 0.133], [0.515, 0.134, 0.928, 0.146], [0.515, 0.148, 0.928, 0.16], [0.515, 0.162, 0.553, 0.173]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 321, "edu_l1_label": "IOS"}, {"txt": "w2(X,P) =", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10400000, "bbox": [[0.532, 0.193, 0.616, 0.208]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 46, 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["text"], "label": "formula", "web_segment_id": 44, "global_sentence_id": 329, "edu_l1_label": "IOS"}, {"txt": "C", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10400000, "bbox": [[0.897, 0.197, 0.908, 0.204]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 45, "global_sentence_id": 330, "edu_l1_label": "IOS"}, {"txt": "2πaxop", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10400000, "bbox": [[0.645, 0.239, 0.71, 0.255]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 41, "global_sentence_id": 331, "edu_l1_label": "IOS"}, {"txt": "where TM = Md2/2πℏdenotes the Talbot time.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10400000, "bbox": [[0.515, 0.293, 0.866, 0.305]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 332, "edu_l1_label": "EDU_O"}, {"txt": "For the fnal fringe pattern, we propagate the Wigner function w2 freely for another time t and then obtain the position distribution by integrating over the momentum coordinate.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10500000, "bbox": [[0.531, 0.307, 0.928, 0.319], [0.515, 0.32, 0.928, 0.332], [0.515, 0.334, 0.928, 0.346], [0.515, 0.348, 0.596, 0.359]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 333, "edu_l1_label": "IOS"}, {"txt": "We arrive at", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10500000, "bbox": [[0.596, 0.348, 0.695, 0.359]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 334, "edu_l1_label": "EDU_O"}, {"txt": "w3(X) =", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.54, 0.377, 0.602, 0.391]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 37, "global_sentence_id": 335, "edu_l1_label": "IOS"}, {"txt": "一", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.594, 0.41, 0.604, 0.416]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 35, "global_sentence_id": 336, "edu_l1_label": "IOS"}, {"txt": "B(x.y)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.633, 0.399, 0.683, 0.416]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 36, "global_sentence_id": 337, "edu_l1_label": "IOS"}, {"txt": "j,j+n", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.645, 0.41, 0.687, 0.422]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 34, "global_sentence_id": 338, "edu_l1_label": "IOS"}, {"txt": "(B8)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.895, 0.406, 0.928, 0.418]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 13, "global_sentence_id": 339, "edu_l1_label": "IOS"}, {"txt": "j,n", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10600000, "bbox": [[0.61, 0.422, 0.632, 0.434]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 33, "global_sentence_id": 340, "edu_l1_label": "IOS"}, {"txt": "Here, we introduce the abbreviation An,k(X) for the Fourier integral of the Gaussian initial Wigner function over P. The classical fringe pattern resulting from the kernel (B6) is obtained by replacing An,k(X) →An,0(X).Explicitly, we have", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10700000, "bbox": [[0.51, 0.442, 0.932, 0.513]]}]}, "tags": ["figure_caption"], "label": "content", "web_segment_id": 7, "global_sentence_id": 341, "edu_l1_label": "IOS"}, {"txt": "\\begin{aligned} { A _ { n , k } ( X ) } & { { } = \\int \\frac { \\mathrm { d } P } { 2 \\pi \\sigma _ { X } \\sigma _ { P } } e ^ { - i n k t P / \\hbar T _ { M } - ( P + k h / a ) ^ { 2 } / 2 \\sigma _ { P } ^ { 2 } } \\, e ^ { - [ X - P ( t + t _ { 0 } ) / M - k d t _ { 0 } / T _ { M } ] ^ { 2 } / 2 \\sigma _ { X } ^ { 2 } } } \\\\ { } & { { } = e ^ { 2 \\pi i n k t / T _ { M } } \\int \\frac { \\mathrm { d } P } { 2 \\pi \\sigma _ { X } \\sigma _ { P } } e ^ { - i n d t P / M T _ { M } - P ^ { 2 } / 2 \\sigma _ { P } ^ { 2 } } \\, e ^ { - \\left| X - P ( t + t _ { 0 } ) / M + k d t / T _ { M } \\right| ^ { 2 } / 2 \\sigma _ { X } ^ { 2 } } } \\\\ \\end{aligned}", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10800000, "bbox": [[0.185, 0.545, 0.801, 0.612]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 52, "global_sentence_id": 342, "edu_l1_label": "IOS"}, {"txt": "(B9)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10800000, "bbox": [[0.895, 0.594, 0.928, 0.606]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 9, "global_sentence_id": 343, "edu_l1_label": "EDU_O"}, {"txt": "To simplify the Gaussian terms in the exponent, which we need to integrate over P, we defne the auxiliary rescaled position and momentum widths,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 10900000, "bbox": [[0.071, 0.622, 0.928, 0.634], [0.071, 0.636, 0.309, 0.648]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 344, "edu_l1_label": "IOS"}, {"txt": "\\tilde { \\sigma } _ { P } ^ { 2 } = \\frac { 1 } { \\frac { 1 } { \\sigma _ { P } ^ { 2 } } + \\frac { ( t + t _ { 0 } ) ^ { 2 } } { M ^ { 2 } \\sigma _ { X } ^ { 2 } } } = \\frac { \\sigma _ { P } ^ { 2 } } { 1 + \\left[ \\frac { \\sigma _ { P } ( t + t _ { 0 } ) } { M \\sigma _ { X } } \\right] ^ { 2 } } ,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11000000, "bbox": [[0.331, 0.651, 0.627, 0.694]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 51, "global_sentence_id": 345, "edu_l1_label": "IOS"}, {"txt": "(B10)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11000000, "bbox": [[0.886, 0.666, 0.928, 0.677]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 10, "global_sentence_id": 346, "edu_l1_label": "EDU_O"}, {"txt": "\\tilde { \\sigma } _ { X } ^ { 2 } = \\frac { \\sigma _ { X } ^ { 2 } } { 1 - \\frac { \\tilde { \\sigma } _ { P } ^ { 2 } ( t + t _ { 0 } ) ^ { 2 } } { M ^ { 2 } \\sigma _ { X } ^ { 2 } } } = \\sigma _ { X } ^ { 2 } + \\left[ \\frac { \\sigma _ { P } ( t + t _ { 0 } ) } { M } \\right] ^ { 2 } ,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11100000, "bbox": [[0.342, 0.698, 0.666, 0.74]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 50, "global_sentence_id": 347, "edu_l1_label": "IOS"}, {"txt": "(B11)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11100000, "bbox": [[0.886, 0.712, 0.928, 0.724]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 12, "global_sentence_id": 348, "edu_l1_label": "EDU_O"}, {"txt": "which preserve σ˜X σ˜P = σXσP , as one can easily check.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11200000, "bbox": [[0.071, 0.75, 0.48, 0.762]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 349, "edu_l1_label": "IOS"}, {"txt": "Abbreviating temporarily Xk = X + kdt/TM, the Gaussianterms in the exponent can then be expanded as", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11200000, "bbox": [[0.48, 0.75, 0.928, 0.762], [0.071, 0.764, 0.42, 0.776]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 350, "edu_l1_label": "IOS"}, {"txt": "20%", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11300000, "bbox": [[0.193, 0.797, 0.226, 0.818]]}]}, "tags": ["text"], "label": "O", "web_segment_id": 27, "global_sentence_id": 351, "edu_l1_label": "EDU_O"}, {"txt": "[Xk = P(t + to)/M]²", "language": "english", 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"edu_l1_label": "EDU_O"}, {"txt": "Here, we introduced the n-th order fringe reduction factor Rn and what will become the magnifed fringe period D,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11700000, "bbox": [[0.071, 0.224, 0.919, 0.236]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 9, "global_sentence_id": 379, "edu_l1_label": "IOS"}, {"txt": "(B14)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11800000, "bbox": [[0.886, 0.25, 0.93, 0.266]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 29, "global_sentence_id": 380, "edu_l1_label": "EDU_O"}, {"txt": "D = \\frac { d } { 1 - \\frac { \\tilde { \\sigma } _ { P } ^ { 2 } t ( t + t _ { 0 } ) } { M ^ { 2 } \\sigma _ { X } ^ { 2 } } } = d \\frac { ( t + t _ { 0 } ) ^ { 2 } + ( M \\sigma _ { X } / \\sigma _ { P } ) ^ { 2 } } { t _ { 0 } ( t + t _ { 0 } ) + ( M \\sigma _ { X } / \\sigma _ { P } ) ^ { 2 } } .", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 11900000, "bbox": [[0.313, 0.265, 0.678, 0.306]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 38, "global_sentence_id": 381, "edu_l1_label": "IOS"}, {"txt": "Now we can put everything together and obtain the quantum interferogram and the classical fringe pattern,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12000000, "bbox": [[0.071, 0.318, 0.863, 0.33]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 382, "edu_l1_label": "IOS"}, {"txt": "(B15)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12100000, "bbox": [[0.886, 0.277, 0.93, 0.292]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 28, "global_sentence_id": 383, "edu_l1_label": "IOS"}, {"txt": 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"global_sentence_id": 390, "edu_l1_label": "IOS"}, {"txt": "(B16)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12200000, "bbox": [[0.886, 0.351, 0.929, 0.368]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 27, "global_sentence_id": 391, "edu_l1_label": "IOS"}, {"txt": "(B17)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12200000, "bbox": [[0.886, 0.394, 0.928, 0.406]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 12, "global_sentence_id": 392, "edu_l1_label": "IOS"}, {"txt": "72", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12200000, "bbox": [[0.334, 0.411, 0.351, 0.42]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 22, "global_sentence_id": 393, "edu_l1_label": "EDU_O"}, {"txt": "These are the expressions we use to evaluate the fringe patterns in the main text.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12300000, "bbox": [[0.071, 0.43, 0.667, 0.442]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 394, "edu_l1_label": "IOS"}, {"txt": "For an appreciable fringe visibility, we need to have sizeable Rn=0, implying [σXt/d(t + t0)] ≪1.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12300000, "bbox": [[0.667, 0.43, 0.928, 0.442], [0.071, 0.444, 0.539, 0.456]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 395, "edu_l1_label": "IOS"}, {"txt": "At the same time, we also aim for a strong fringemagnifcation, implying that t ≫t0 so that D ≈dt/t0 ≫d.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12300000, "bbox": [[0.539, 0.444, 0.928, 0.456], [0.071, 0.458, 0.52, 0.469]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 396, "edu_l1_label": "IOS"}, {"txt": "The consequence is that we need to have σX ≪d forvisible fringes.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12300000, "bbox": [[0.52, 0.458, 0.928, 0.469], [0.071, 0.471, 0.176, 0.483]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 397, "edu_l1_label": "IOS"}, {"txt": "A tradeof must be chosen carefully here.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12300000, "bbox": [[0.176, 0.471, 0.484, 0.483]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 398, "edu_l1_label": "IOS"}, {"txt": "In order to highlight the regime in which the quantum and the classical fringe patterns coincide approximately, we consider the scenario in which the nanoparticle is initially well localized, σX ≲d, but has a broad momentumdistribution compared to the difraction scale, σP ≫2πℏ/d.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12400000, "bbox": [[0.088, 0.485, 0.928, 0.497], [0.071, 0.498, 0.928, 0.51], [0.071, 0.512, 0.501, 0.524]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 399, "edu_l1_label": "IOS"}, {"txt": "This implies that σP (t+t0)/MσX ≫(d/σX)(t+t0)/TM ≳1 for the relevant t, t0, and we may then approximate", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12400000, "bbox": [[0.501, 0.512, 0.928, 0.526], [0.071, 0.526, 0.463, 0.537]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 400, "edu_l1_label": "IOS"}, {"txt": "σ˜X ≈σP (tM + t0),σ˜P ≈Mt +σ tX0⇒D ≈dt +t0 t0,Rn ≈e−2π2n2σX2t2/d2(t+t0)2.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12500000, "bbox": [[0.18, 0.558, 0.307, 0.57], [0.327, 0.558, 0.411, 0.579], [0.452, 0.557, 0.469, 0.578], [0.507, 0.558, 0.601, 0.57], [0.621, 0.558, 0.819, 0.57]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 13, "global_sentence_id": 401, "edu_l1_label": "IOS"}, {"txt": "(B18)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12500000, "bbox": [[0.886, 0.558, 0.928, 0.57]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 13, "global_sentence_id": 402, "edu_l1_label": "EDU_O"}, {"txt": "These approximations are already applied in the above expressions (A10) and (A11).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12600000, "bbox": [[0.071, 0.59, 0.692, 0.601]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 403, "edu_l1_label": "IOS"}, {"txt": "If we can also neglect the small position displacements (of order d) in the broad Gaussian envelope of (B16), we obtain the quantum expression", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12600000, "bbox": [[0.692, 0.59, 0.928, 0.601], [0.071, 0.603, 0.891, 0.615]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 8, "global_sentence_id": 404, "edu_l1_label": "IOS"}, {"txt": "w _ { 3 } ( X ) \\approx { \\frac { e ^ { - [ M X / \\sigma _ { P } ( t + t _ { 0 } ) ] ^ { 2 } / 2 } } { \\sqrt { 2 \\pi } \\sigma _ { P } ( t + t _ { 0 } ) / M } } \\sum _ { n } e ^ { 2 \\pi i n X / D + i n \\phi _ { z } } R _ { n } B _ { n } \\left[ n { \\frac { t t _ { 0 } } { T _ { M } ( t + t _ { 0 } ) } } \\right] .", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12700000, "bbox": [[0.245, 0.623, 0.755, 0.662]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 39, "global_sentence_id": 405, "edu_l1_label": "IOS"}, {"txt": "(B19)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12700000, "bbox": [[0.886, 0.639, 0.928, 0.651]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 14, "global_sentence_id": 406, "edu_l1_label": "EDU_O"}, {"txt": "For the corresponding classical version, simply set the argument of Bn[.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.071, 0.675, 0.598, 0.687]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 407, "edu_l1_label": "IOS"}, {"txt": ".", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.598, 0.675, 0.606, 0.687]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 408, "edu_l1_label": "IOS"}, {"txt": ".]", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.606, 0.675, 0.618, 0.687]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 409, "edu_l1_label": "IOS"}, {"txt": "→Bn(0).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.618, 0.675, 0.692, 0.687]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 410, "edu_l1_label": "IOS"}, {"txt": "Comparing the fnal expression(B19) to its classical counterpart tells us that we need to have Bn=0(ξ) = const for non-classical behaviour in thisapproximated scenario.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.692, 0.675, 0.928, 0.687], [0.071, 0.689, 0.928, 0.701], [0.071, 0.703, 0.24, 0.715]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 411, "edu_l1_label": "IOS"}, {"txt": "This implies that we need to condition on more than a single pair of ±N-th difraction ordersfor non-classical fringe terms to occur.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12800000, "bbox": [[0.24, 0.703, 0.928, 0.715], [0.071, 0.716, 0.355, 0.728]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 412, "edu_l1_label": "IOS"}, {"txt": "We prove this statement by assuming that we condition on only the ±N-th difraction order, i.e., the only non-zerograting coefcients are B−(xN,y,)−", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 12900000, "bbox": [[0.088, 0.73, 0.928, 0.742], [0.071, 0.746, 0.29, 0.766]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 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"formula", "web_segment_id": 11, "global_sentence_id": 420, "edu_l1_label": "IOS"}, {"txt": "= ò710", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13100000, "bbox": [[0.236, 0.803, 0.284, 0.818]]}]}, "tags": ["text"], "label": "O", "web_segment_id": 15, "global_sentence_id": 421, "edu_l1_label": "EDU_O"}, {"txt": "(x,y)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13100000, "bbox": [[0.38, 0.801, 0.413, 0.809]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 16, "global_sentence_id": 422, "edu_l1_label": "IOS"}, {"txt": "Hence the quantum and the classical fringe patterns are indistinguishable.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13200000, "bbox": [[0.071, 0.832, 0.615, 0.844]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 423, "edu_l1_label": "IOS"}, {"txt": "Quantum behaviour arises if we allow for mixed terms between at least two diferent difraction orders, e.g., we condition on ±1 and ±2.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13300000, "bbox": [[0.088, 0.846, 0.928, 0.858], [0.071, 0.86, 0.255, 0.871]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 424, "edu_l1_label": "IOS"}, {"txt": "This implies that genuine quantum interference is more prominent the greater odd-integerTalbot coefcients such as B±1, B±3 are in magnitude.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13300000, "bbox": [[0.255, 0.86, 0.928, 0.871], [0.071, 0.873, 0.472, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 425, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": 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"language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13500000, "bbox": [[0.088, 0.151, 0.928, 0.163], [0.071, 0.165, 0.928, 0.177], [0.071, 0.178, 0.928, 0.19], [0.071, 0.192, 0.928, 0.204], [0.071, 0.206, 0.212, 0.218]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 0, "global_sentence_id": 428, "edu_l1_label": "IOS"}, {"txt": "Explicitly, the modifcation contributes a Lindblad dissipator to the free evolution of the reduced centre-of-mass state, ∂tρcm = −i[ Pˆ 2/2Mℏ, ρcm] + Lρcm, the position representation of which reads as", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13600000, "bbox": [[0.088, 0.219, 0.928, 0.231], [0.071, 0.233, 0.703, 0.245]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 7, "global_sentence_id": 429, "edu_l1_label": "IOS"}, {"txt": "(X|Cpcm|X′) = -[T(0) = T(X = X′)](X|ecm|X′),", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13700000, "bbox": [[0.098, 0.265, 0.461, 0.279]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 22, "global_sentence_id": 430, "edu_l1_label": "IOS"}, {"txt": "7", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13700000, "bbox": [[0.601, 0.261, 0.616, 0.269]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 23, "global_sentence_id": 431, "edu_l1_label": "EDU_O"}, {"txt": "d3q", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13700000, "bbox": [[0.631, 0.255, 0.67, 0.271]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 24, "global_sentence_id": 432, "edu_l1_label": "IOS"}, {"txt": "(C1)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13700000, "bbox": [[0.894, 0.266, 0.928, 0.277]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 9, "global_sentence_id": 433, "edu_l1_label": "IOS"}, {"txt": "mánJ J", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13700000, "bbox": [[0.554, 0.273, 0.624, 0.289]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 21, "global_sentence_id": 434, "edu_l1_label": "IOS"}, {"txt": "Here, τ0 is a time parameter, σq a momentum width parameter (here in units of wavenumbers), and m0 is a referencemass taken to be that of the electron in previous comparative studies.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13800000, "bbox": [[0.071, 0.299, 0.928, 0.311], [0.071, 0.313, 0.59, 0.325]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 435, "edu_l1_label": "IOS"}, {"txt": "Accordingly, we also restrict to super-atomic momentum widths, 1/σq ≳1 nm.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13800000, "bbox": [[0.59, 0.313, 0.928, 0.325], [0.071, 0.327, 0.318, 0.338]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 436, "edu_l1_label": "IOS"}, {"txt": "The integrand contains the Fourier transform of the particle’s mass density.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13800000, "bbox": [[0.318, 0.327, 0.893, 0.338]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 437, "edu_l1_label": "IOS"}, {"txt": "As-suming a homogeneous mass density for our disc-shaped spheroidal particle of volume V = 4πRM2bM/3, the Fouriertransform can be shown to take the simple form", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13800000, "bbox": [[0.893, 0.327, 0.928, 0.338], [0.071, 0.34, 0.928, 0.352], [0.071, 0.354, 0.424, 0.366]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 2, "global_sentence_id": 438, "edu_l1_label": "IOS"}, {"txt": "\\tilde { \\varrho } _ { M } ( \\mathrm { \\bold ~ q ~ } ) = \\frac { M } { V } \\int _ { V } \\mathrm { d } ^ { 3 } r \\, e ^ { - i \\mathrm { \\bold ~ q ~ \\cdot r ~ } } = 3 M \\frac { j _ { 1 } \\left[ \\sqrt { ( q _ { \\bot } R _ { M } ) ^ { 2 } + ( q _ { z } b _ { M } ) ^ { 2 } } \\right] } { \\sqrt { ( q _ { \\bot } R _ { M } ) ^ { 2 } + ( q _ { z } b _ { M } ) ^ { 2 } } } ,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13900000, "bbox": [[0.273, 0.373, 0.725, 0.417]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 28, "global_sentence_id": 439, "edu_l1_label": "IOS"}, {"txt": "(C2)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 13900000, "bbox": [[0.894, 0.394, 0.928, 0.406]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 8, "global_sentence_id": 440, "edu_l1_label": "EDU_O"}, {"txt": "where j1 is a spherical Bessel function and q⊥=qqx2 + qy2.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14000000, "bbox": [[0.071, 0.433, 0.512, 0.445]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 441, "edu_l1_label": "IOS"}, {"txt": "Noting that the function vanishes for q⊥≫1/RM andthat the relevant spatial coherences are confned to the atomic scale in our case, |X −X′| ≲d, we can Taylor-expandthe Fourier exponential in (C1).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14000000, "bbox": [[0.512, 0.433, 0.928, 0.445], [0.071, 0.451, 0.928, 0.463], [0.071, 0.465, 0.305, 0.477]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 442, "edu_l1_label": "IOS"}, {"txt": "To lowest non-vanishing order, we obtain", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14000000, "bbox": [[0.305, 0.465, 0.614, 0.477]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 1, "global_sentence_id": 443, "edu_l1_label": "IOS"}, {"txt": "\\begin{aligned} { \\Gamma ( 0 ) - \\Gamma ( X - X ^ { \\prime } ) } & { { } \\approx \\frac { 0 \\varepsilon M ^ { 2 } ( X - X ^ { \\prime } ) ^ { 2 } } { 2 \\alpha _ { 0 } ^ { 2 } \\tau } \\int _ { - \\infty } ^ { \\infty } d \\xi _ { 3 } \\int _ { 0 } ^ { \\infty } d \\eta _ { 1 } \\eta _ { - } ^ { 2 } \\frac { e ^ { 4 \\phi _ { 1 } ^ { 2 } + i \\xi _ { 1 } ^ { 2 } + i \\xi _ { 1 } ^ { 2 } } } { ( 2 \\pi \\sigma _ { 0 } ^ { 2 / 2 } ) } \\frac { \\left[ \\sqrt { | q _ { 1 } R _ { 1 } | ^ { 2 } - | q _ { 2 } | q _ { 1 } | ^ { 2 } } \\right] } { \\sqrt { | q _ { 1 } ^ { 2 } R _ { 1 } | ^ { 2 } + | q _ { 2 } | q _ { 1 } | ^ { 2 } } } } & { { } \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\, \\quad \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\, \\mathrm { ( 3 ) } } \\\\ { } & { { } = \\frac { 0 \\lambda ^ { 2 } \\sigma _ { 1 } ^ { 2 } ( X - X ^ { \\prime } ) ^ { 2 } } { 2 \\sqrt { | q _ { 1 } ^ { 2 } + | q _ { 2 } | q _ { 1 } | ^ { 2 } } } T ( \\sigma _ { 1 } R _ { 1 1 } , \\sigma _ { 1 } d _ { 2 } ) , \\quad \\, \\, \\, \\, \\, \\, \\mathfrak { I } ( \\eta _ { 1 } , \\beta ) = \\int _ { - } ^ { \\infty } d \\xi _ { 1 } ^ { 2 } \\eta _ { 1 } ^ { 2 } e ^ { - | q _ { 1 } ^ {", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14100000, "bbox": [[0.061, 0.486, 0.938, 0.571]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 27, "global_sentence_id": 444, "edu_l1_label": "IOS"}, {"txt": "The remaining double integral I can be evaluated numerically for each argument (α, β).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14200000, "bbox": [[0.071, 0.584, 0.717, 0.596]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 6, "global_sentence_id": 445, "edu_l1_label": "IOS"}, {"txt": "The contribution of the dissipator (C1) to the free evolution is most conveniently expressed in the characteristic function representation of the Wigner function.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14300000, "bbox": [[0.088, 0.598, 0.928, 0.61], [0.071, 0.612, 0.423, 0.623]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 446, "edu_l1_label": "IOS"}, {"txt": "This was done in Ref.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14300000, "bbox": [[0.423, 0.612, 0.596, 0.623]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 447, "edu_l1_label": "IOS"}, {"txt": "[25] in the limit of an arbitrarily incoherent initial particle state, σP →∞, which remains valid here as long as the net broadening of the Gaussian envelope dueto (C1) is negligible.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14300000, "bbox": [[0.596, 0.612, 0.928, 0.623], [0.071, 0.625, 0.928, 0.637], [0.071, 0.639, 0.224, 0.651]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 448, "edu_l1_label": "IOS"}, {"txt": "This is indeed the case here, since we assume σP ≫2πℏ/d > ℏσq.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14300000, "bbox": [[0.224, 0.639, 0.727, 0.651]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 3, "global_sentence_id": 449, "edu_l1_label": "IOS"}, {"txt": "As a result, the reductionfactors Rn in the quantum fringe 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"edu_l1_label": "IOS"}, {"txt": "2√2πm3π [Tu(t + to)]", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14500000, "bbox": [[0.597, 0.694, 0.785, 0.713]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 11, "global_sentence_id": 460, "edu_l1_label": "IOS"}, {"txt": "Z(aqRm,00", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14500000, "bbox": [[0.796, 0.689, 0.879, 0.701]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 13, "global_sentence_id": 461, "edu_l1_label": "IOS"}, {"txt": "The macroscopicity µ of a quantum experiment is then given by the greatest value of the time parameter τ0, maximizedwith respect to σq, that is ruled out by an observation of quantum interference fringes.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14600000, "bbox": [[0.071, 0.727, 0.928, 0.738], [0.071, 0.74, 0.71, 0.752]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 462, "edu_l1_label": "IOS"}, {"txt": "For our proposed case study,we assume that one could observe more than 50% of the predicted quantum fringe contrast of order n = 2 at t = 1 ms and t0 = TM, as depicted in the bottom end of Fig.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14600000, "bbox": [[0.71, 0.74, 0.928, 0.752], [0.071, 0.754, 0.928, 0.766], [0.071, 0.767, 0.449, 0.779]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 463, "edu_l1_label": "IOS"}, {"txt": "2(a).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14600000, "bbox": [[0.449, 0.767, 0.489, 0.779]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 464, "edu_l1_label": "IOS"}, {"txt": "Given σq, this rules out", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14600000, "bbox": [[0.489, 0.767, 0.668, 0.779]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 5, "global_sentence_id": 465, "edu_l1_label": "IOS"}, {"txt": "\\tau _ { 0 } \\leq \\tau _ { \\mathrm { m a x } } ( \\sigma _ { q } ) = \\frac { 6 ( M / m _ { 0 } ) ^ { 2 } } { \\sqrt { 2 \\pi } \\ln 2 } \\frac { t ^ { 2 } } { t + T _ { M } } ( \\sigma _ { q } d ) ^ { 2 } \\mathcal { I } ( \\sigma _ { q } R _ { M } , \\sigma _ { q } b _ { M } ) .", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14700000, "bbox": [[0.282, 0.786, 0.716, 0.822]]}]}, "tags": ["equation"], "label": "formula", "web_segment_id": 26, "global_sentence_id": 466, "edu_l1_label": "IOS"}, {"txt": "(C5)", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14700000, "bbox": [[0.894, 0.8, 0.928, 0.812]]}]}, "tags": ["text"], "label": "formula", "web_segment_id": 10, "global_sentence_id": 467, "edu_l1_label": "EDU_O"}, {"txt": "We numerically maximize to arrive at µ = log10 maxσq τmax(σq) ≈16.3.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14800000, "bbox": [[0.071, 0.832, 0.614, 0.844]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 468, "edu_l1_label": "IOS"}, {"txt": "Bayesian statistical analysis of the mea-surement data from a previous molecule interference experiment resulted in the current record value of 14.0 [10, 59].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14800000, "bbox": [[0.614, 0.832, 0.928, 0.844], [0.071, 0.846, 0.928, 0.858]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 469, "edu_l1_label": "IOS"}, {"txt": "Since µ is a logarithmic quantity, the diference amounts to more than two orders of magnitude in the ruled out timeparameter.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14800000, "bbox": [[0.071, 0.86, 0.928, 0.871], [0.071, 0.873, 0.15, 0.885]]}]}, "tags": ["text"], "label": "content", "web_segment_id": 4, "global_sentence_id": 470, "edu_l1_label": "IOS"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 14900000, "bbox": [[0.911, 0.09, 0.929, 0.1]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 471, "edu_l1_label": "EDU_O"}, {"txt": "[1] C. M. DeWitt and D. Rickles, The Role of Gravitation in Physics:", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.157, 0.485, 0.168], [0.102, 0.17, 0.176, 0.18]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 472, "edu_l1_label": "EDU_O"}, {"txt": " Report from the 1957 Chapel Hill Conference (epubli, 2011).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.176, 0.17, 0.485, 0.18], [0.102, 0.182, 0.2, 0.193]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 473, "edu_l1_label": "EDU_O"}, {"txt": "[2] C. Anastopoulos and B. L. Hu, Probing a gravitational cat state, Class.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.195, 0.485, 0.205], [0.102, 0.207, 0.21, 0.218]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 474, "edu_l1_label": "EDU_O"}, {"txt": "Quant.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.21, 0.207, 0.262, 0.218]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 475, "edu_l1_label": "EDU_O"}, {"txt": "Grav.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.262, 0.207, 0.305, 0.218]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 476, "edu_l1_label": "EDU_O"}, {"txt": "32, 165022 (2015).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.305, 0.207, 0.436, 0.218]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 477, "edu_l1_label": "EDU_O"}, {"txt": "[3] S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroˇs, M. Paternostro, A.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.219, 0.339, 0.23], [0.339, 0.219, 0.485, 0.23], [0.102, 0.232, 0.308, 0.243]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 478, "edu_l1_label": "EDU_O"}, {"txt": "A. Geraci, P. F. Barker,M.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.308, 0.232, 0.485, 0.243], [0.102, 0.244, 0.121, 0.255]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 479, "edu_l1_label": "EDU_O"}, {"txt": "Kim, and G. Milburn, Spin entanglement witness for quantum gravity, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.121, 0.244, 0.485, 0.255], [0.102, 0.257, 0.26, 0.267]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 480, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.26, 0.257, 0.296, 0.267]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 481, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.296, 0.257, 0.334, 0.267]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 482, "edu_l1_label": "EDU_O"}, {"txt": "119, 240401 (2017).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.334, 0.257, 0.474, 0.267]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 483, "edu_l1_label": "EDU_O"}, {"txt": "[4] C. Marletto and V. Vedral, Gravitationally induced entanglement between two massive particles is sufcient evidence of quantum efects in gravity, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.269, 0.485, 0.28], [0.102, 0.282, 0.485, 0.292], [0.102, 0.294, 0.378, 0.305]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 484, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.378, 0.294, 0.413, 0.305]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 485, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.413, 0.294, 0.45, 0.305]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 486, "edu_l1_label": "EDU_O"}, {"txt": "119, 240402 (2017).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.45, 0.294, 0.485, 0.305], [0.102, 0.306, 0.201, 0.317]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 487, "edu_l1_label": "EDU_O"}, {"txt": "[5] A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, Cˇ.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.319, 0.485, 0.33], [0.102, 0.331, 0.118, 0.342]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 488, "edu_l1_label": "EDU_O"}, {"txt": "Brukner, and M. Aspelmeyer, Quantum superposi-tion of massive objects and the quantization of gravity, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.118, 0.331, 0.485, 0.342], [0.102, 0.344, 0.485, 0.354], [0.102, 0.356, 0.139, 0.367]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 489, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.139, 0.356, 0.175, 0.367]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 490, "edu_l1_label": "EDU_O"}, {"txt": "D 98, 126009 (2018).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.175, 0.356, 0.324, 0.367]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 491, "edu_l1_label": "EDU_O"}, {"txt": "[6] M. Carlesso, A. Bassi, M. Paternostro, and H. Ulbricht, Testing the gravitational feld generated by a quantum superposition, New J. Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.369, 0.485, 0.379], [0.102, 0.381, 0.485, 0.392], [0.102, 0.393, 0.292, 0.404]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 492, "edu_l1_label": "EDU_O"}, {"txt": "21, 093052 (2019).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.292, 0.393, 0.423, 0.404]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 493, "edu_l1_label": "EDU_O"}, {"txt": "[7] C. Anastopoulos and B. L. Hu, Quantum superposition of two gravitational cat states, Class.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.406, 0.485, 0.416], [0.102, 0.418, 0.359, 0.429]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 494, "edu_l1_label": "EDU_O"}, {"txt": "Quant.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.359, 0.418, 0.412, 0.429]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 495, "edu_l1_label": "EDU_O"}, {"txt": "Grav.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.412, 0.418, 0.456, 0.429]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 496, "edu_l1_label": "EDU_O"}, {"txt": "37, 235012 (2020).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.456, 0.418, 0.485, 0.429], [0.102, 0.431, 0.201, 0.441]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 497, "edu_l1_label": "EDU_O"}, {"txt": "[8] S. Bose, I. Fuentes, A.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.079, 0.443, 0.247, 0.454]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 498, "edu_l1_label": "EDU_O"}, {"txt": "A. Geraci, S. M. Khan, S. Qvarfort, M. Rademacher, M. Rashid, M. Toroˇs, H. Ulbricht, andC.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.247, 0.443, 0.485, 0.454], [0.102, 0.456, 0.485, 0.466], [0.102, 0.468, 0.118, 0.479]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 499, "edu_l1_label": "EDU_O"}, {"txt": "C. Wanjura, Massive quantum systems as interfaces of quantum mechanics and gravity (2024), arXiv:2311.09218 [quant-ph] [9] M. Arndt and K. Hornberger, Testing the limits of quantum mechanical superpositions, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.118, 0.468, 0.485, 0.479], [0.102, 0.48, 0.485, 0.491], [0.102, 0.493, 0.172, 0.503], [0.079, 0.505, 0.171, 0.516], [0.171, 0.505, 0.333, 0.516], [0.333, 0.505, 0.485, 0.516], [0.102, 0.518, 0.385, 0.528]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 500, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.385, 0.518, 0.428, 0.528]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 501, "edu_l1_label": "EDU_O"}, {"txt": "10, 271 (2014) [10] Y. Y. Fein, P. Geyer, P. Zwick, F. Kia lka, S. Pedalino, M. Mayor, S. Gerlich, and M. Arndt, Quantum superposition of molecules beyond 25 kDa, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.428, 0.518, 0.485, 0.528], [0.102, 0.53, 0.145, 0.541], [0.071, 0.543, 0.485, 0.553], [0.102, 0.555, 0.485, 0.566], [0.102, 0.567, 0.377, 0.578]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 502, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.377, 0.567, 0.42, 0.578]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 503, "edu_l1_label": "EDU_O"}, {"txt": "15, 1242 (2019).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.42, 0.567, 0.485, 0.578], [0.102, 0.58, 0.149, 0.59]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 504, "edu_l1_label": "EDU_O"}, {"txt": "[11] P. Haslinger, N. D¨orre, P. Geyer, J. Rodewald, S. Nimm-richter, and M. Arndt, A universal matter-wave interferometer with optical ionization gratings in the time domain, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.592, 0.485, 0.603], [0.102, 0.605, 0.485, 0.615], [0.102, 0.617, 0.485, 0.628], [0.102, 0.629, 0.175, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 505, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.175, 0.629, 0.217, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 506, "edu_l1_label": "EDU_O"}, {"txt": "9, 144 (2013).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.217, 0.629, 0.316, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 507, "edu_l1_label": "EDU_O"}, {"txt": "[12] S.Nimmrichter, K.Hornberger, P. Haslinger,and M. Arndt, Testing spontaneous localization theories with matter-wave interferometry , Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.642, 0.217, 0.653], [0.231, 0.642, 0.34, 0.653], [0.354, 0.642, 0.368, 0.653], [0.38, 0.642, 0.485, 0.653], [0.102, 0.654, 0.485, 0.665], [0.102, 0.667, 0.291, 0.677], [0.29, 0.667, 0.34, 0.677]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 508, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.348, 0.667, 0.379, 0.677]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 509, "edu_l1_label": "EDU_O"}, {"txt": "A 83, 043621 (2011).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.379, 0.667, 0.485, 0.677], [0.102, 0.679, 0.149, 0.69]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 510, "edu_l1_label": "EDU_O"}, {"txt": "[13] A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Models of wave-function collapse, underlying theories, and experimental tests, Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.692, 0.485, 0.702], [0.102, 0.704, 0.485, 0.715], [0.102, 0.716, 0.341, 0.727]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 511, "edu_l1_label": "EDU_O"}, {"txt": "Mod.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.341, 0.716, 0.383, 0.727]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 512, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.383, 0.716, 0.427, 0.727]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 513, "edu_l1_label": "EDU_O"}, {"txt": "85, 471 (2013).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.427, 0.716, 0.485, 0.727], [0.102, 0.729, 0.149, 0.74]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 514, "edu_l1_label": "EDU_O"}, {"txt": "[14] A. Bassi, M. Dorato, and H. Ulbricht, Collapse models: A theoretical, experimental and philosophical review, Entropy 25, 645 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.741, 0.485, 0.752], [0.102, 0.754, 0.485, 0.764], [0.102, 0.766, 0.247, 0.777]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 515, "edu_l1_label": "EDU_O"}, {"txt": "[15] U. Deli´c, M. Reisenbauer, K. Dare, D. Grass, V. Vuleti´c,N.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.779, 0.485, 0.789], [0.102, 0.791, 0.118, 0.802]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 516, "edu_l1_label": "EDU_O"}, {"txt": "Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparticle to the motional quantum ground state, Science 367, 892 (2020).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.118, 0.791, 0.485, 0.802], [0.102, 0.803, 0.485, 0.814], [0.102, 0.816, 0.248, 0.827]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 517, "edu_l1_label": "EDU_O"}, {"txt": "[16] M. Perdriat, C. Pellet-Mary, P. Huillery, L. Rondin, and G. H´etet, Spin-mechanics with nitrogen-vacancy centersand trapped particles, Micromachines 12, 651 (2021).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.828, 0.485, 0.839], [0.102, 0.841, 0.485, 0.851], [0.102, 0.853, 0.465, 0.864]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 518, "edu_l1_label": "EDU_O"}, {"txt": "[17] J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez-", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.071, 0.866, 0.485, 0.876]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 3, "global_sentence_id": 519, "edu_l1_label": "EDU_O"}, {"txt": "Ballestero, A. de los R´ıos Sommer, N. Meyer, R. Quidant,O.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.545, 0.157, 0.928, 0.168], [0.545, 0.17, 0.562, 0.18]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 520, "edu_l1_label": "EDU_O"}, {"txt": "Romero-Isart, R. Reimann, and L. Novotny, Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.562, 0.17, 0.928, 0.18], [0.545, 0.182, 0.928, 0.193], [0.545, 0.195, 0.732, 0.205]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 521, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.732, 0.195, 0.774, 0.205]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 522, "edu_l1_label": "EDU_O"}, {"txt": "19, 1009 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.774, 0.195, 0.89, 0.205]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 523, "edu_l1_label": "EDU_O"}, {"txt": "[18] M. Perdriat, C. C. Rusconi, T. Delord, P. Huillery, C. Pellet-Mary, B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.207, 0.928, 0.218], [0.545, 0.219, 0.67, 0.23]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 524, "edu_l1_label": "EDU_O"}, {"txt": "A. Stickler, and G. H´etet, Spin read-out of the motion of levitated electrically rotated diamonds (2023), arXiv:2309.01545 [quant-ph].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.67, 0.219, 0.928, 0.23], [0.545, 0.232, 0.928, 0.243], [0.545, 0.244, 0.842, 0.255]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 525, "edu_l1_label": "EDU_O"}, {"txt": "[19] D. S. Bykov, L. Dania, F. Goschin, and T. E. Northup, A nanoparticle stored with an atomic ion in a linear paul trap (2024), arXiv:2403.02034 [quant-ph].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.257, 0.928, 0.267], [0.545, 0.269, 0.928, 0.28], [0.545, 0.282, 0.827, 0.292]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 526, "edu_l1_label": "EDU_O"}, {"txt": "[20] Y. Jin, K. Shen, P. Ju, X. Gao, C. Zu, A. J. Grine, and T. Li, Quantum control and berry phase of electron spins in rotating levitated diamonds in high vacuum, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.294, 0.788, 0.305], [0.788, 0.294, 0.928, 0.305], [0.545, 0.306, 0.928, 0.317], [0.545, 0.319, 0.928, 0.33], [0.545, 0.331, 0.575, 0.342]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 527, "edu_l1_label": "EDU_O"}, {"txt": "Commun.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.575, 0.331, 0.646, 0.342]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 528, "edu_l1_label": "EDU_O"}, {"txt": "15, 5063 (2024).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.646, 0.331, 0.762, 0.342]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 529, "edu_l1_label": "EDU_O"}, {"txt": "[21] M. Rossi, A. Militaru, N. C. Zambon, A. Riera-Campeny, O. Romero-Isart, M. Frimmer, and L. Novotny, Quantum delocalization of a levitated nanoparticle (2024), arXiv:2408.01264 [quant-ph].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.344, 0.928, 0.354], [0.545, 0.356, 0.928, 0.367], [0.545, 0.369, 0.928, 0.379], [0.545, 0.381, 0.741, 0.392]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 530, "edu_l1_label": "EDU_O"}, {"txt": "[22] R. Mufato, T. S. Georgescu, M. Carlesso, M. Paternostro, and H. Ulbricht, Coherent expansion of the motional state of a massive nanoparticle beyond its linear dimensions (2024), arXiv:2408.09596 [quant-ph].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.393, 0.928, 0.404], [0.545, 0.406, 0.928, 0.416], [0.545, 0.418, 0.928, 0.429], [0.545, 0.431, 0.831, 0.441]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 531, "edu_l1_label": "EDU_O"}, {"txt": "[23] O. Romero-Isart, A. C. Pfanzer, F. Blaser, R. Kaltenbaek, N. Kiesel, M. Aspelmeyer, and J. I. Cirac, Large Quantum Superpositions and Interference of Massive Nanometer-Sized Objects, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.443, 0.562, 0.454], [0.581, 0.443, 0.674, 0.454], [0.697, 0.443, 0.713, 0.454], [0.732, 0.443, 0.747, 0.454], [0.766, 0.443, 0.826, 0.454], [0.848, 0.443, 0.863, 0.454], [0.882, 0.443, 0.928, 0.454], [0.545, 0.456, 0.662, 0.466], [0.662, 0.456, 0.928, 0.466], [0.545, 0.468, 0.928, 0.479], [0.545, 0.48, 0.849, 0.491]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 532, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.849, 0.48, 0.888, 0.491]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 533, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.888, 0.48, 0.928, 0.491]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 534, "edu_l1_label": "EDU_O"}, {"txt": "107, 020405 (2011).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.545, 0.493, 0.68, 0.503]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 535, "edu_l1_label": "EDU_O"}, {"txt": "[24] S.Nimmrichter, P. Haslinger, K. Hornberger,and M. Arndt, Concept of an ionizing time-domain matterwave interferometer, New J. Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.505, 0.661, 0.516], [0.675, 0.505, 0.688, 0.516], [0.7, 0.505, 0.768, 0.516], [0.782, 0.505, 0.798, 0.516], [0.81, 0.505, 0.928, 0.516], [0.545, 0.518, 0.928, 0.528], [0.545, 0.53, 0.778, 0.541]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 536, "edu_l1_label": "EDU_O"}, {"txt": "13, 75002 (2011).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.778, 0.53, 0.901, 0.541]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 537, "edu_l1_label": "EDU_O"}, {"txt": "[25] J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Near-feld interferometry of a free-falling nanoparticle from a point-like source, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.543, 0.928, 0.553], [0.545, 0.555, 0.928, 0.566], [0.545, 0.567, 0.794, 0.578]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 538, "edu_l1_label": "EDU_O"}, {"txt": "Commun.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.794, 0.567, 0.868, 0.578]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 539, "edu_l1_label": "EDU_O"}, {"txt": "5, 4788 (2014).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.868, 0.567, 0.928, 0.578], [0.545, 0.58, 0.593, 0.59]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 540, "edu_l1_label": "EDU_O"}, {"txt": "[26] C. Wan, M. Scala, G. W. Morley, ATM.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.592, 0.836, 0.603]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 541, "edu_l1_label": "EDU_O"}, {"txt": "A. Rahman, H. Ulbricht, J. Bateman, P. F. Barker, S. Bose, and M. S. Kim, Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.836, 0.592, 0.928, 0.603], [0.545, 0.605, 0.928, 0.615], [0.545, 0.617, 0.928, 0.628], [0.545, 0.629, 0.762, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 542, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.762, 0.629, 0.799, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 543, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.799, 0.629, 0.838, 0.64]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 544, "edu_l1_label": "EDU_O"}, {"txt": "117, 143003 (2016).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.838, 0.629, 0.928, 0.64], [0.545, 0.642, 0.593, 0.653]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 545, "edu_l1_label": "EDU_O"}, {"txt": "[27] O. Romero-Isart, Coherent infation for large quantum superpositions of levitated microspheres, New J. Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.654, 0.928, 0.665], [0.545, 0.667, 0.928, 0.677]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 546, "edu_l1_label": "EDU_O"}, {"txt": "19, 123029 (2017).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.545, 0.679, 0.672, 0.69]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 547, "edu_l1_label": "EDU_O"}, {"txt": "[28] R. Kaltenbaek et al., Research campaign: Macroscopic quantum resonators (maqro), Quant.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.692, 0.928, 0.702], [0.545, 0.704, 0.807, 0.715]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 548, "edu_l1_label": "EDU_O"}, {"txt": "Sci.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.807, 0.704, 0.84, 0.715]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 549, "edu_l1_label": "EDU_O"}, {"txt": "Technol.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.84, 0.704, 0.906, 0.715]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 550, "edu_l1_label": "EDU_O"}, {"txt": "8, 014006 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.906, 0.704, 0.928, 0.715], [0.545, 0.716, 0.644, 0.727]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 551, "edu_l1_label": "EDU_O"}, {"txt": "[29] M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.729, 0.928, 0.74], [0.545, 0.741, 0.928, 0.752], [0.545, 0.754, 0.928, 0.764], [0.545, 0.766, 0.615, 0.777]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 552, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.615, 0.766, 0.65, 0.777]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 553, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.65, 0.766, 0.688, 0.777]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 554, "edu_l1_label": "EDU_O"}, {"txt": "132, 023601 (2024).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.688, 0.766, 0.829, 0.777]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 555, "edu_l1_label": "EDU_O"}, {"txt": "[30] J. Wardak, T. Georgescu, G. Gasbarri, A. Belenchia, and H. Ulbricht, Nanoparticle interferometer by throw and catch, Atoms 12, 10.3390/atoms12020007 (2024).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.779, 0.928, 0.789], [0.545, 0.791, 0.928, 0.802], [0.545, 0.803, 0.88, 0.814]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 556, "edu_l1_label": "EDU_O"}, {"txt": "[31] M. O. E. Steiner, J. S. Pedernales, and M. B. Plenio, Pentacene-doped naphthalene for levitated optomechanics (2024), arXiv:2405.13869 [quant-ph].", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.816, 0.928, 0.827], [0.545, 0.828, 0.928, 0.839], [0.545, 0.841, 0.816, 0.851]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 557, "edu_l1_label": "EDU_O"}, {"txt": "[32] C. Davisson and L. H. Germer, Difraction of electrons by a crystal of nickel, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.515, 0.853, 0.928, 0.864], [0.545, 0.866, 0.733, 0.876]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 1, "global_sentence_id": 558, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.733, 0.866, 0.769, 0.876]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 1, "global_sentence_id": 559, "edu_l1_label": "EDU_O"}, {"txt": "30, 705 (1927).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15000000, "bbox": [[0.769, 0.866, 0.877, 0.876]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 1, "global_sentence_id": 560, "edu_l1_label": "EDU_O"}, {"txt": "header", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.911, 0.09, 0.928, 0.099]]}]}, "tags": ["header"], "label": "O", "web_segment_id": -1, "global_sentence_id": 561, "edu_l1_label": "EDU_O"}, {"txt": "[33] C. Kisielowski et al., Detection of Single Atoms and Buried Defects in Three Dimensions by AberrationCorrected Electron Microscope with 0.5-˚AInformation Limit, Microsc.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.122, 0.485, 0.132], [0.102, 0.134, 0.485, 0.145], [0.102, 0.147, 0.397, 0.157], [0.397, 0.147, 0.485, 0.157], [0.102, 0.159, 0.205, 0.17]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 7, "global_sentence_id": 562, "edu_l1_label": "EDU_O"}, {"txt": "Microanal.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.205, 0.159, 0.282, 0.17]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 7, "global_sentence_id": 563, "edu_l1_label": "EDU_O"}, {"txt": "14, 469 (2008).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.282, 0.159, 0.39, 0.17]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 7, "global_sentence_id": 564, "edu_l1_label": "EDU_O"}, {"txt": "[34] L. Jin, J. Barthel, C.-L. Jia, and K. W. Urban, Atomic resolution imaging of YAlO3:", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.171, 0.485, 0.182], [0.102, 0.184, 0.304, 0.194]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 5, "global_sentence_id": 565, "edu_l1_label": "EDU_O"}, {"txt": " Ce in the chromatic and spherical aberration corrected PICO electron microscope, Ultramicroscopy 176, 99 (2017).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.304, 0.184, 0.485, 0.194], [0.102, 0.196, 0.485, 0.207], [0.102, 0.209, 0.322, 0.219]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 5, "global_sentence_id": 566, "edu_l1_label": "EDU_O"}, {"txt": "[35] K. W. Urban, J. Barthel, L. Houben, C.-L. Jia, L. Jin, M. Lentzen, S.-B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.221, 0.485, 0.232], [0.102, 0.234, 0.233, 0.244]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 4, "global_sentence_id": 567, "edu_l1_label": "EDU_O"}, {"txt": "Mi, A. Thust, and K. Tillmann, Progress in atomic-resolution aberration corrected conventional transmission electron microscopy (CTEM), Prog.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.233, 0.234, 0.485, 0.244], [0.102, 0.246, 0.485, 0.257], [0.102, 0.258, 0.485, 0.269], [0.102, 0.271, 0.138, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 4, "global_sentence_id": 568, "edu_l1_label": "EDU_O"}, {"txt": "Mater.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.138, 0.271, 0.189, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 4, "global_sentence_id": 569, "edu_l1_label": "EDU_O"}, {"txt": "Sci.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.189, 0.271, 0.218, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 4, "global_sentence_id": 570, "edu_l1_label": "EDU_O"}, {"txt": "133, 101037 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.218, 0.271, 0.358, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 4, "global_sentence_id": 571, "edu_l1_label": "EDU_O"}, {"txt": "[36] R. Ishikawa, S. Morishita, T. Tanigaki, N. Shibata, and Y. Ikuhara, Spatial and phase resolution in electron microscopy, Microscopy 72, 78 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.283, 0.485, 0.294], [0.102, 0.296, 0.485, 0.306], [0.102, 0.308, 0.345, 0.319]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 10, "global_sentence_id": 572, "edu_l1_label": "EDU_O"}, {"txt": "[37] S. Tsujino, On the brightness, transverse emittance, andtransversecoherenceoffeld emission beam, J. Vac.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.32, 0.485, 0.331], [0.102, 0.333, 0.358, 0.344], [0.373, 0.333, 0.43, 0.344], [0.444, 0.333, 0.485, 0.344], [0.102, 0.345, 0.149, 0.356]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 6, "global_sentence_id": 573, "edu_l1_label": "EDU_O"}, {"txt": "Sci.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.149, 0.345, 0.178, 0.356]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 6, "global_sentence_id": 574, "edu_l1_label": "EDU_O"}, {"txt": "Technol.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.178, 0.345, 0.24, 0.356]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 6, "global_sentence_id": 575, "edu_l1_label": "EDU_O"}, {"txt": "B 40, 030801 (2022).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.24, 0.345, 0.387, 0.356]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 6, "global_sentence_id": 576, "edu_l1_label": "EDU_O"}, {"txt": "[38] L. Reimer and H. Kohl, Transmission Electron Microscopy (Springer Verlag, 2008).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.358, 0.127, 0.368], [0.127, 0.358, 0.384, 0.368], [0.395, 0.358, 0.45, 0.368], [0.46, 0.358, 0.485, 0.368], [0.102, 0.37, 0.327, 0.381]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 13, "global_sentence_id": 577, "edu_l1_label": "EDU_O"}, {"txt": "[39] V. A.Lobastov, R.Srinivasan, and A. H. Zewail, Four-dimensional ultrafast electron microscopy, Proc.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.383, 0.118, 0.393], [0.132, 0.383, 0.228, 0.393], [0.245, 0.383, 0.349, 0.393], [0.363, 0.383, 0.388, 0.393], [0.403, 0.383, 0.418, 0.393], [0.433, 0.383, 0.449, 0.393], [0.463, 0.383, 0.485, 0.393], [0.102, 0.395, 0.33, 0.406], [0.33, 0.395, 0.395, 0.406], [0.395, 0.395, 0.485, 0.406], [0.102, 0.407, 0.138, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 12, "global_sentence_id": 578, "edu_l1_label": "EDU_O"}, {"txt": "Natl.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.138, 0.407, 0.177, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 12, "global_sentence_id": 579, "edu_l1_label": "EDU_O"}, {"txt": "Acad.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.177, 0.407, 0.221, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 12, "global_sentence_id": 580, "edu_l1_label": "EDU_O"}, {"txt": "Sci.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.221, 0.407, 0.251, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 12, "global_sentence_id": 581, "edu_l1_label": "EDU_O"}, {"txt": "U.S.A. 102, 7069 (2005).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.251, 0.407, 0.425, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 12, "global_sentence_id": 582, "edu_l1_label": "EDU_O"}, {"txt": "[40] A. H. Zewail, 4D ultrafast electron difraction, crystallography, and microscopy, Annu.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.42, 0.485, 0.431], [0.102, 0.432, 0.306, 0.443]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 11, "global_sentence_id": 583, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.306, 0.432, 0.342, 0.443]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 11, "global_sentence_id": 584, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.342, 0.432, 0.386, 0.443]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 11, "global_sentence_id": 585, "edu_l1_label": "EDU_O"}, {"txt": "Chem.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.386, 0.432, 0.435, 0.443]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 11, "global_sentence_id": 586, "edu_l1_label": "EDU_O"}, {"txt": "57, 65 (2006).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.435, 0.432, 0.485, 0.443], [0.102, 0.445, 0.149, 0.455]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 11, "global_sentence_id": 587, "edu_l1_label": "EDU_O"}, {"txt": "[41] G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Pomarico, R. J. Lamb, D. Mcgrouther, I. Kaminer, B. Barwick, F. Javier Garc´ıa de Abajo, and F. Carbone, At-tosecond coherent control of free-electron wave functions using semi-infnite light felds, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.457, 0.485, 0.468], [0.102, 0.47, 0.485, 0.48], [0.102, 0.482, 0.485, 0.493], [0.102, 0.494, 0.485, 0.505], [0.102, 0.507, 0.351, 0.518]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 588, "edu_l1_label": "EDU_O"}, {"txt": "Commun.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.351, 0.507, 0.425, 0.518]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 589, "edu_l1_label": "EDU_O"}, {"txt": "9, 2694 (2018).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.425, 0.507, 0.485, 0.518], [0.102, 0.519, 0.149, 0.53]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 0, "global_sentence_id": 590, "edu_l1_label": "EDU_O"}, {"txt": "[42] S. Mori, H. Nakajima, A. Kotani, and K. Harada, Recent advances in small-angle electron difraction and Lorentz microscopy, Microscopy 70, 59 (2021).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.532, 0.485, 0.542], [0.102, 0.544, 0.485, 0.555], [0.102, 0.557, 0.362, 0.567]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 8, "global_sentence_id": 591, "edu_l1_label": "EDU_O"}, {"txt": "[43] X. Llopart, J. Alozy, R. Ballabriga, M. Campbell, R. Casanova, V.Gromov, E. Heijne, T. Poikela, E. Santin, V. Sriskaran, et al., Timepix4, a large area pixel detector readout chip which can be tiled on 4 sides providing sub-200 ps timestamp binning, J. Instrum.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.569, 0.129, 0.58], [0.129, 0.569, 0.183, 0.58], [0.196, 0.569, 0.261, 0.58], [0.273, 0.569, 0.3, 0.58], [0.3, 0.569, 0.374, 0.58], [0.386, 0.569, 0.485, 0.58], [0.102, 0.581, 0.118, 0.592], [0.13, 0.581, 0.198, 0.592], [0.213, 0.581, 0.3, 0.592], [0.314, 0.581, 0.329, 0.592], [0.342, 0.581, 0.389, 0.592], [0.404, 0.581, 0.419, 0.592], [0.432, 0.581, 0.485, 0.592], [0.102, 0.594, 0.485, 0.604], [0.102, 0.606, 0.485, 0.617], [0.102, 0.619, 0.458, 0.629]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 1, "global_sentence_id": 592, "edu_l1_label": "EDU_O"}, {"txt": "17, C01044 (2022).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.458, 0.619, 0.485, 0.629], [0.102, 0.631, 0.204, 0.642]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 1, "global_sentence_id": 593, "edu_l1_label": "EDU_O"}, {"txt": "[44] S. Lindner, P. Juschitz, J. Rieser, Y. Y. Fein, M. Debiossac, M. A. Ciampini, M. Aspelmeyer, and N. Kiesel, Hollow-core fber loading of nanoparticles into ultra-high vacuum, Appl.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.644, 0.485, 0.654], [0.102, 0.656, 0.485, 0.667], [0.102, 0.668, 0.485, 0.679], [0.102, 0.681, 0.201, 0.691]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 594, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.201, 0.681, 0.243, 0.691]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 595, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.243, 0.681, 0.281, 0.691]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 596, "edu_l1_label": "EDU_O"}, {"txt": "124 (2024).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.281, 0.681, 0.366, 0.691]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 2, "global_sentence_id": 597, "edu_l1_label": "EDU_O"}, {"txt": "[45] L. Dania, K. Heidegger, D. S. Bykov, G. Cerchiari, G. Araneda, and T. E. Northup, Position measurement of a levitated nanoparticle via interference with its mirror image, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.693, 0.336, 0.704], [0.336, 0.693, 0.393, 0.704], [0.393, 0.693, 0.485, 0.704], [0.102, 0.706, 0.485, 0.716], [0.102, 0.718, 0.485, 0.729], [0.102, 0.731, 0.188, 0.741]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 3, "global_sentence_id": 598, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.188, 0.731, 0.224, 0.741]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 3, "global_sentence_id": 599, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.224, 0.731, 0.262, 0.741]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 3, "global_sentence_id": 600, "edu_l1_label": "EDU_O"}, {"txt": "129, 013601 (2022).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.262, 0.731, 0.402, 0.741]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 3, "global_sentence_id": 601, "edu_l1_label": "EDU_O"}, {"txt": "[46] T. Danz, T. Domr¨ose,andC.Ropers,Ultrafast nanoimaging of the order parameter in a structural phase transition, Science 371, 371 (2021).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.743, 0.118, 0.754], [0.131, 0.743, 0.17, 0.754], [0.186, 0.743, 0.201, 0.754], [0.215, 0.743, 0.411, 0.754], [0.424, 0.743, 0.485, 0.754], [0.102, 0.755, 0.485, 0.766], [0.102, 0.768, 0.343, 0.778]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 9, "global_sentence_id": 602, "edu_l1_label": "EDU_O"}, {"txt": "[47] J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.071, 0.78, 0.485, 0.791]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 15, "global_sentence_id": 603, "edu_l1_label": "EDU_O"}, {"txt": "Optomechanics with levitated particles, Rep. Prog.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.545, 0.122, 0.887, 0.132]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 604, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.887, 0.122, 0.928, 0.132]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 605, "edu_l1_label": "EDU_O"}, {"txt": "83, 026401 (2020) [48] E. Bonvin, L. Devaud, M. Rossi, A. Militaru, L. Dania, D. S. Bykov, M. Teller, T. E. Northup, L. Novotny, and M. Frimmer, Hybrid paul-optical trap with large optical access for levitated optomechanics, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.545, 0.134, 0.667, 0.145], [0.515, 0.147, 0.928, 0.157], [0.545, 0.159, 0.928, 0.17], [0.545, 0.171, 0.928, 0.182], [0.545, 0.184, 0.833, 0.194]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 606, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.833, 0.184, 0.871, 0.194]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 607, "edu_l1_label": "EDU_O"}, {"txt": "Res.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.871, 0.184, 0.907, 0.194]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 608, "edu_l1_label": "EDU_O"}, {"txt": "6, 043129 (2024).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.907, 0.184, 0.928, 0.194], [0.545, 0.196, 0.644, 0.207]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 609, "edu_l1_label": "EDU_O"}, {"txt": "[49] C. Lee, Y. Ikematsu, and D. Shindo, Measurement of mean free paths for inelastic electron scattering of Si and SiO2, Journal of Electron Microscopy 51, 143 (2002).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.209, 0.928, 0.219], [0.545, 0.221, 0.928, 0.232], [0.545, 0.234, 0.908, 0.244]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 610, "edu_l1_label": "EDU_O"}, {"txt": "[50] C. T. Koch, W. Sigle, R. H¨oschen, M. Ru¨hle, E. Es-sers, G. Benner, and M. Matijevic, SESAM: Exploring the Frontiers of Electron Microscopy, Microsc.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.246, 0.928, 0.257], [0.545, 0.258, 0.928, 0.269], [0.545, 0.271, 0.852, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 611, "edu_l1_label": "EDU_O"}, {"txt": "Microanal.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.852, 0.271, 0.928, 0.281]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 612, "edu_l1_label": "EDU_O"}, {"txt": "12, 506 (2006).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.545, 0.283, 0.648, 0.294]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 613, "edu_l1_label": "EDU_O"}, {"txt": "[51] A. Ruiz Caridad, R. Erni, A. Vogel, and M. D. Rossell, Applications of a novel electron energy flter combined with a hybrid-pixel direct electron detector for the analysis of functional oxides by STEM/EELS and energyfltered imaging, Micron 160, 103331 (2022).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.296, 0.928, 0.306], [0.545, 0.308, 0.928, 0.319], [0.545, 0.32, 0.928, 0.331], [0.545, 0.333, 0.928, 0.344], [0.545, 0.345, 0.849, 0.356]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 614, "edu_l1_label": "EDU_O"}, {"txt": "[52] B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.358, 0.561, 0.368]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 615, "edu_l1_label": "EDU_O"}, {"txt": "A. Stickler, K. Hornberger, and M. Kim, Quantum rotations of nanoparticles, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.561, 0.358, 0.928, 0.368], [0.545, 0.37, 0.755, 0.381]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 616, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.755, 0.37, 0.79, 0.381]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 617, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.79, 0.37, 0.831, 0.381]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 618, "edu_l1_label": "EDU_O"}, {"txt": "3, 589 (2021).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.831, 0.37, 0.928, 0.381]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 619, "edu_l1_label": "EDU_O"}, {"txt": "[53] B. Schrinski, B.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.383, 0.656, 0.393]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 620, "edu_l1_label": "EDU_O"}, {"txt": "A. Stickler, and K. Hornberger, Interferometric control of nanorotor alignment, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.656, 0.383, 0.928, 0.393], [0.545, 0.395, 0.875, 0.406]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 621, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.875, 0.395, 0.911, 0.406]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 622, "edu_l1_label": "EDU_O"}, {"txt": "A 105, L021502 (2022).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.911, 0.395, 0.928, 0.406], [0.545, 0.407, 0.69, 0.418]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 623, "edu_l1_label": "EDU_O"}, {"txt": "[54] M. Kamba, R. Shimizu, and K. Aikawa, Nanoscale feedback control of six degrees of freedom of a near-sphere, Nat.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.42, 0.928, 0.431], [0.545, 0.432, 0.928, 0.443], [0.545, 0.445, 0.575, 0.455]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 624, "edu_l1_label": "EDU_O"}, {"txt": "Commun.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.575, 0.445, 0.646, 0.455]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 625, "edu_l1_label": "EDU_O"}, {"txt": "14, 7943 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.646, 0.445, 0.762, 0.455]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 626, "edu_l1_label": "EDU_O"}, {"txt": "[55] R. Egerton, R. McLeod, F. Wang, and M. Malac, Basic questions related to electron-induced sputtering in the tem, Ultramicroscopy 110, 991 (2010).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.457, 0.928, 0.468], [0.545, 0.47, 0.928, 0.48], [0.545, 0.482, 0.809, 0.493]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 627, "edu_l1_label": "EDU_O"}, {"txt": "[56] E. Hebestreit, R. Reimann, M. Frimmer, and L. Novotny, Measuringtheinternaltemperatureofalevitated nanoparticle in high vacuum, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.494, 0.928, 0.505], [0.545, 0.507, 0.928, 0.518], [0.545, 0.519, 0.791, 0.53]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 628, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.791, 0.519, 0.828, 0.53]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 629, "edu_l1_label": "EDU_O"}, {"txt": "A 97, 043803 (2018).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.828, 0.519, 0.928, 0.53], [0.545, 0.532, 0.593, 0.542]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 630, "edu_l1_label": "EDU_O"}, {"txt": "[57] K. Hornberger, J. E. Sipe, and M. Arndt, Theory of decoherence in a matter wave talbot-lau interferometer, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.544, 0.928, 0.555], [0.545, 0.557, 0.928, 0.567]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 631, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.545, 0.569, 0.576, 0.58]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 632, "edu_l1_label": "EDU_O"}, {"txt": "A 70, 053608 (2004).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.576, 0.569, 0.724, 0.58]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 633, "edu_l1_label": "EDU_O"}, {"txt": "[58] K. Reidy, J. D. Thomsen, and F. M. Ross, Perspectives on ultra-high vacuum transmission electron microscopy of dynamic crystal growth phenomena, Prog.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.581, 0.928, 0.592], [0.545, 0.594, 0.928, 0.604], [0.545, 0.606, 0.849, 0.617]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 634, "edu_l1_label": "EDU_O"}, {"txt": "Mater.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.849, 0.606, 0.899, 0.617]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 635, "edu_l1_label": "EDU_O"}, {"txt": "Sci.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.899, 0.606, 0.928, 0.617]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 636, "edu_l1_label": "EDU_O"}, {"txt": "139, 101163 (2023).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.545, 0.619, 0.68, 0.629]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 637, "edu_l1_label": "EDU_O"}, {"txt": "[59] B. Schrinski,S.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.631, 0.561, 0.642], [0.573, 0.631, 0.666, 0.642]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 638, "edu_l1_label": "EDU_O"}, {"txt": "Nimmrichter,andK.Hornberger, Quantum-classical  hypothesis tests in macroscopic matter-wave interferometry, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.679, 0.631, 0.928, 0.642], [0.545, 0.644, 0.669, 0.654], [0.685, 0.644, 0.756, 0.654], [0.771, 0.644, 0.802, 0.654], [0.818, 0.644, 0.831, 0.654], [0.846, 0.644, 0.928, 0.654], [0.545, 0.656, 0.78, 0.667]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 639, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.78, 0.656, 0.818, 0.667]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 640, "edu_l1_label": "EDU_O"}, {"txt": "Res.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.818, 0.656, 0.854, 0.667]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 641, "edu_l1_label": "EDU_O"}, {"txt": "2, 033034 (2020).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.854, 0.656, 0.928, 0.667], [0.545, 0.668, 0.593, 0.679]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 642, "edu_l1_label": "EDU_O"}, {"txt": "[60] S. Nimmrichter andK.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.681, 0.558, 0.691], [0.573, 0.681, 0.659, 0.691], [0.674, 0.681, 0.73, 0.691]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 643, "edu_l1_label": "EDU_O"}, {"txt": "Hornberger, Macroscopicity of mechanicalquantum superposition states, Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.745, 0.681, 0.825, 0.691], [0.84, 0.681, 0.928, 0.691], [0.545, 0.693, 0.564, 0.704], [0.58, 0.693, 0.593, 0.704], [0.61, 0.693, 0.761, 0.704], [0.778, 0.693, 0.868, 0.704], [0.885, 0.693, 0.928, 0.704], [0.545, 0.706, 0.583, 0.716]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 644, "edu_l1_label": "EDU_O"}, {"txt": "Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.583, 0.706, 0.619, 0.716]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 645, "edu_l1_label": "EDU_O"}, {"txt": "Lett.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.619, 0.706, 0.657, 0.716]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 646, "edu_l1_label": "EDU_O"}, {"txt": "110, 160403 (2013).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.657, 0.706, 0.797, 0.716]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 647, "edu_l1_label": "EDU_O"}, {"txt": "[61] A. G. Jackson, Handbook of crystallography: for electron microscopists and others (Springer New York, 1991).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.718, 0.928, 0.729], [0.545, 0.731, 0.903, 0.741]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 648, "edu_l1_label": "EDU_O"}, {"txt": "[62]  K. Hornberger, S. Gerlich, P. Haslinger, S. Nimmrichter, and M. Arndt, Colloquium: Quantum interference of clusters and molecules, Rev.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.743, 0.539, 0.754], [0.539, 0.743, 0.545, 0.754], [0.545, 0.743, 0.928, 0.754], [0.545, 0.755, 0.742, 0.766], [0.756, 0.755, 0.928, 0.766], [0.545, 0.768, 0.736, 0.778]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 649, "edu_l1_label": "EDU_O"}, {"txt": "Mod.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.736, 0.768, 0.777, 0.778]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 650, "edu_l1_label": "EDU_O"}, {"txt": "Phys.", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.777, 0.768, 0.819, 0.778]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 651, "edu_l1_label": "EDU_O"}, {"txt": "84, 157 (2012).", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.819, 0.768, 0.927, 0.778]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 652, "edu_l1_label": "EDU_O"}, {"txt": "[63] Here we assume that the centre-of-mass state is pure, e.g.,", "language": "english", "position": {"pdf_position": [{"page_number": 0, "shape": [1650, 1275], "position_id": 15100000, "bbox": [[0.515, 0.78, 0.928, 0.791]]}]}, "tags": ["text"], "label": "reference", "web_segment_id": 14, "global_sentence_id": 653, "edu_l1_label": "EDU_O"}], "type": "PDF"}
# Electron-Enabled Nanoparticle Difraction
## I.INTRODUCTION
## II.PROPOSED EXPERIMENT
## III.RELEVANT SYSTEMATIC EFFECTS
## IV.DECOHERENCE ESTIMATES
## V. DISCUSSION
## Appendix A: Efective grating transformation
## Appendix B: Phase-space description of the matter-wave difraction scheme
