Abstract

We demonstrate fast and efficient neutral atom rearrangements in an optical tweezer-trap array, using an enhanced hologram generation algorithm. The conventional Gerchberg-Saxton (GS) algorithm is modified to include zero-padding hologram expansion for optical tweezer sharpness, weighted iteration feedback for reduced crosstalk, and phase induction for successive phase continuity. With the new GS algorithm, we experimentally demonstrate defect-free formation of 2D atom arrays with various geometries, achieving a high loading probability of 0.98 for up to N ∼ 30 atoms. Furthermore, the hologram movie calculation speed is enhanced to cover a computational scalability up to 𝒪(103).

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

H. Kim, Y. Park, K. Kim, H.-S. Sim, and J. Ahn, “Detailed balance of thermalization dynamics in Rydberg atom quantum simulators,” Phys. Rev. Lett. 120, 180502 (2018).
[Crossref]

S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
[Crossref]

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref]

2017 (2)

W. Lee, H. Kim, and J. Ahn, “Defect-free atomic array formation using the Hungarian matching algorithm,” Phys. Rev. A 95, 053424 (2017).
[Crossref]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

2016 (9)

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
[Crossref] [PubMed]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref] [PubMed]

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
[Crossref]

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24(6), 6249–6264 (2016).
[Crossref]

H. Tamura, T. Unakami, J. He, Y. Miyamoto, and K. Nakagawa, “Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements,” Opt. Express 24(8), 8132–8141 (2016).
[Crossref] [PubMed]

W. Lee, H. Kim, and J. Ahn, “Three-dimensional rearrangement of single atoms using actively controlled optical microtraps,” Opt. Express 24(9), 9816–9825 (2016).
[Crossref]

P. Zupancic, P. M. Preiss, R. Ma, A. Lukin, M. E. Tai, M. Rispoli, R. Islam, and M. Greiner, “Ultra-precise holographic beam shaping for microscopic quantum control,” Opt. Express 24(13), 13881–13893 (2016).
[Crossref]

2015 (2)

K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2(4), 343–346 (2015).
[Crossref]

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
[Crossref]

2014 (2)

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

S. P. Poland, N. Krstajić, R. D. Knight, R. K. Henderson, and S. M. Ameer-Beg, “Development of a doubly weighted Gerchberg-Saxton algorithm for use in multibeam imaging applications,” Opt. Lett. 39(8), 2431–2434 (2014).
[Crossref]

2013 (3)

2012 (2)

M. Persson, D. Engstrom, and M. Goksor, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20(20), 22334–22343 (2012).
[Crossref]

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a Single Atom in an Optical Tweezer to Its Quantum Ground State,” Phys. Rev. X 2, 041014 (2012).

2011 (1)

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

2010 (1)

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photon. 4, 388–394 (2010).
[Crossref]

2007 (1)

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

2006 (1)

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

2005 (2)

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express 13(14), 5434–5439 (2005).
[Crossref] [PubMed]

W. Graeme and C. Johannes, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
[Crossref]

2004 (1)

2003 (3)

D. McGloin, G.C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11(2), 158–166 (2003).
[Crossref]

G. Shabtay, “Three-dimensional beam forming and Ewald’s surfaces,” Opt. Comm. 226(1–6), 33–37 (2003).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

2002 (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Ahn, J.

H. Kim, Y. Park, K. Kim, H.-S. Sim, and J. Ahn, “Detailed balance of thermalization dynamics in Rydberg atom quantum simulators,” Phys. Rev. Lett. 120, 180502 (2018).
[Crossref]

W. Lee, H. Kim, and J. Ahn, “Defect-free atomic array formation using the Hungarian matching algorithm,” Phys. Rev. A 95, 053424 (2017).
[Crossref]

H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
[Crossref] [PubMed]

W. Lee, H. Kim, and J. Ahn, “Three-dimensional rearrangement of single atoms using actively controlled optical microtraps,” Opt. Express 24(9), 9816–9825 (2016).
[Crossref]

Ameer-Beg, S. M.

Anschuetz, E. R.

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

Armellin, C.

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

Arnold, A. S.

Barredo, D.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref]

V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref] [PubMed]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

Béguin, L.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

Bernien, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

Bowman, R. W.

Boyer, V.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

Browaeys, A.

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref]

V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref] [PubMed]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

Brown, M. O.

M. O. Brown, T. Thiele, C. Kiehl, T.-W. Hsu, and C. A. Regal, “Scaling atom array assembly with grey molasses,” arXiv:1811.01448 (2018).

Burchianti, A.

S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
[Crossref]

Carr, A. W.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
[Crossref]

Cassettari, D.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

Chandrashekar, C. M.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

Chen, H.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H.- T. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Chen, Z.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H.- T. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Choi, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

Cizmar, T.

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photon. 4, 388–394 (2010).
[Crossref]

Clark, T. W.

Conclave, S.

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Heilemann, M.

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Huser, T.

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
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V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
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D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
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V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
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H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
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Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
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Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
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Lee, H.

H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
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W. Lee, H. Kim, and J. Ahn, “Defect-free atomic array formation using the Hungarian matching algorithm,” Phys. Rev. A 95, 053424 (2017).
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H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
[Crossref] [PubMed]

W. Lee, H. Kim, and J. Ahn, “Three-dimensional rearrangement of single atoms using actively controlled optical microtraps,” Opt. Express 24(9), 9816–9825 (2016).
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A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a Single Atom in an Optical Tweezer to Its Quantum Ground State,” Phys. Rev. X 2, 041014 (2012).

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H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
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T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
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V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
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Lukin, A.

Lukin, M. D.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
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Macrí, T.

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
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JP. Covey, IS. Madjarov, A. Cooper, and M. Endres, “2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays,” arXiv:1811.06014 (2018).

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T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
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T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photon. 4, 388–394 (2010).
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Melville, H.

Mercier, R.

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
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Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
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S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
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Naik, DS.

S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
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Omran, A.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
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Padgett, M. J.

Park, Y.

H. Kim, Y. Park, K. Kim, H.-S. Sim, and J. Ahn, “Detailed balance of thermalization dynamics in Rydberg atom quantum simulators,” Phys. Rev. Lett. 120, 180502 (2018).
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K. Kim, J. Yoon, and Y. Park, “Simultaneous 3D visualization and position tracking of optically trapped particles using optical diffraction tomography,” Optica 2(4), 343–346 (2015).
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Pichler, H.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
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T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
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Preiss, P. M.

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H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
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F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

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A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a Single Atom in an Optical Tweezer to Its Quantum Ground State,” Phys. Rev. X 2, 041014 (2012).

M. O. Brown, T. Thiele, C. Kiehl, T.-W. Hsu, and C. A. Regal, “Scaling atom array assembly with grey molasses,” arXiv:1811.01448 (2018).

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Ritsch-Marte, M.

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S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
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Roichman, Y.

Rosi, S.

S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
[Crossref]

Saffman, M.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
[Crossref]

Schmid, B.

Schuler, M.

V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

Schüttpelz, M.

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
[Crossref]

Schwartz, S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

Senko, C.

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

Shabtay, G.

G. Shabtay, “Three-dimensional beam forming and Ewald’s surfaces,” Opt. Comm. 226(1–6), 33–37 (2003).
[Crossref]

Sibbett, W.

Sim, H.-S.

H. Kim, Y. Park, K. Kim, H.-S. Sim, and J. Ahn, “Detailed balance of thermalization dynamics in Rydberg atom quantum simulators,” Phys. Rev. Lett. 120, 180502 (2018).
[Crossref]

Sinclair, G.

Smirne, G.

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

Song, Y.

H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
[Crossref] [PubMed]

Sortais, Y. R. P.

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

Spahn, C.

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
[Crossref]

Spalding, G.C.

Tai, M. E.

Tamura, H.

Thalhammer, G.

Thiele, T.

M. O. Brown, T. Thiele, C. Kiehl, T.-W. Hsu, and C. A. Regal, “Scaling atom array assembly with grey molasses,” arXiv:1811.01448 (2018).

Tuchendler, C.

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

Unakami, T.

Vernier, A.

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

Voigt, F. F.

Vuletic, V.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

Wang, H.- T.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H.- T. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Wolfson, D. L.

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
[Crossref]

Xia, T.

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
[Crossref]

Xu, J.

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H.- T. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Yao, E.

Yoon, J.

Zibrov, A. S.

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

Zupancic, P.

J. Opt. (1)

H. Chen, Y. Guo, Z. Chen, J. Hao, J. Xu, H.- T. Wang, and J. Ding, “Holographic optical tweezers obtained by using the three-dimensional Gerchberg-Saxton algorithm,” J. Opt. 15(3), 035401 (2013).
[Crossref]

Nat. Commun. (2)

H. Kim, W. Lee, H. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis using dynamic holographic optical tweezers,” Nat. Commun. 7, 13317 (2016).
[Crossref] [PubMed]

R. Diekmann, D. L. Wolfson, C. Spahn, M. Heilemann, M. Schüttpelz, and T. Huser, “Nanoscopy of bacterial cells immobilized by holographic optical tweezers,” Nat. Commun. 7, 13711 (2016).
[Crossref]

Nat. Photon. (2)

K. Dholakia and T. Cizmar, “Shaping the future of manipulation,” Nat. Photon. 5, 335–342 (2011).
[Crossref]

T. Cizmar, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photon. 4, 388–394 (2010).
[Crossref]

Nature (4)

D. Barredo, V. Lienhard, S. de Léséleuc, T. Lahaye, and A. Browaeys, “Synthetic three-dimensional atomic structures assembled atom by atom,” Nature 561, 79–82 (2018).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810–816 (2003).
[Crossref] [PubMed]

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin,“Probing many-body dynamics on a 51-atom quantum simulator,” Nature 551, 579–584 (2017).
[Crossref] [PubMed]

H. Labuhn, D. Barredo, S. Ravets, S. de Léséleuc, T. Macrí, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature 534, 667–670 (2016).
[Crossref]

New J. Phys. (1)

W. Graeme and C. Johannes, “Experimental demonstration of holographic three-dimensional light shaping using a Gerchberg-Saxton algorithm,” New J. Phys. 7, 117 (2005).
[Crossref]

Opt. Comm. (1)

G. Shabtay, “Three-dimensional beam forming and Ewald’s surfaces,” Opt. Comm. 226(1–6), 33–37 (2003).
[Crossref]

Opt. Commun. (1)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207(1–6), 169–175 (2002).
[Crossref]

Opt. Express (10)

D. McGloin, G.C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11(2), 158–166 (2003).
[Crossref]

H. Tamura, T. Unakami, J. He, Y. Miyamoto, and K. Nakagawa, “Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements,” Opt. Express 24(8), 8132–8141 (2016).
[Crossref] [PubMed]

Y. Roichman and D. G. Grier, “Holographic assembly of quasicrystalline photonic heterostructures,” Opt. Express 13(14), 5434–5439 (2005).
[Crossref] [PubMed]

T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24(6), 6249–6264 (2016).
[Crossref]

G. Sinclair, J. Leach, P. Jordan, G. Gibson, E. Yao, Z. J. Laczik, M. J. Padgett, and J. Courtial, “Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping,” Opt. Express 12(8), 1665–1670 (2004).
[Crossref] [PubMed]

F. O. Fahrbach, F. F. Voigt, B. Schmid, F. Helmchen, and J. Huisken, “Rapid 3D light-sheet microscopy with a tunable lens,” Opt. Express 21(18), 21010–21026 (2013).
[Crossref] [PubMed]

M. Persson, D. Engstrom, and M. Goksor, “Reducing the effect of pixel crosstalk in phase only spatial light modulators,” Opt. Express 20(20), 22334–22343 (2012).
[Crossref]

P. Zupancic, P. M. Preiss, R. Ma, A. Lukin, M. E. Tai, M. Rispoli, R. Islam, and M. Greiner, “Ultra-precise holographic beam shaping for microscopic quantum control,” Opt. Express 24(13), 13881–13893 (2016).
[Crossref]

W. Lee, H. Kim, and J. Ahn, “Three-dimensional rearrangement of single atoms using actively controlled optical microtraps,” Opt. Express 24(9), 9816–9825 (2016).
[Crossref]

G. Thalhammer, R. W. Bowman, G. D. Love, M. J. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express 21(2), 1779–1797 (2013).
[Crossref]

Opt. Lett. (1)

Optica (1)

Phys. Rev. A (3)

V. Boyer, R. M. Godun, G. Smirne, D. Cassettari, C. M. Chandrashekar, A. B. Deb, Z. J. Laczik, and C. J. Foot, “Dynamic manipulation of Bose-Einstein condensates with a spatial light modulator,” Phys. Rev. A 73, 031402(R) (2006).
[Crossref]

Y. R. P. Sortais, H. Marion, C. Tuchendler, A. M. Lance, M. Lamare, P. Fournet, C. Armellin, R. Mercier, G. Messin, A. Browaeys, and P. Grangier, “Diffraction-limited optics for single-atom manipulation,” Phys. Rev. A 75, 013406 (2007).
[Crossref]

W. Lee, H. Kim, and J. Ahn, “Defect-free atomic array formation using the Hungarian matching algorithm,” Phys. Rev. A 95, 053424 (2017).
[Crossref]

Phys. Rev. Lett. (2)

T. Xia, M. Lichtman, K. Maller, A. W. Carr, M. J. Piotrowicz, L. Isenhower, and M. Saffman, “Randomized Benchmarking of Single-Qubit Gates in a 2D Array of Neutral-Atom Qubits,” Phys. Rev. Lett. 114, 100503 (2015).
[Crossref]

H. Kim, Y. Park, K. Kim, H.-S. Sim, and J. Ahn, “Detailed balance of thermalization dynamics in Rydberg atom quantum simulators,” Phys. Rev. Lett. 120, 180502 (2018).
[Crossref]

Phys. Rev. X (3)

V. Lienhard, S. de Léséleuc, D. Barredo, T. Lahaye, A. Browaeys, M. Schuler, L. Henry, and A. M. Läuchli, “Observing the Space-and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions,” Phys. Rev. X 8, 021070 (2018).

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-Atom Trapping in Holographic 2D Arrays of Microtraps with Arbitrary Geometries,” Phys. Rev. X 4, 021034 (2014).

A. M. Kaufman, B. J. Lester, and C. A. Regal, “Cooling a Single Atom in an Optical Tweezer to Its Quantum Ground State,” Phys. Rev. X 2, 041014 (2012).

Science (2)

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354, 1024–1027 (2016).
[Crossref] [PubMed]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354, 1021–1023 (2016).
[Crossref] [PubMed]

Scientific reports (1)

S. Rosi, A. Burchianti, S. Conclave, DS. Naik, G. Roati, C. Fort, and F. Minardi, “Λ-enhanced grey molasses on the D2 transition of Rubidium-87 atoms,” Scientific reports 8, 1301 (2018).
[Crossref]

Other (2)

JP. Covey, IS. Madjarov, A. Cooper, and M. Endres, “2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays,” arXiv:1811.06014 (2018).

M. O. Brown, T. Thiele, C. Kiehl, T.-W. Hsu, and C. A. Regal, “Scaling atom array assembly with grey molasses,” arXiv:1811.01448 (2018).

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Figures (8)

Fig. 1
Fig. 1 (a) Experimental setup for generating 2D 87Rb atom array and fluorescence imaging. (b) Entire block diagram of the modified GS algorithm, where the mainly modified parts, “Weighting”, “Induction”, and “Zero-pedding”, are highlighted with red letters. (c) An example of transport path planning (middle figure) from a random array of atoms (left figure) to a target butterfly configuration (right figure). The bipartite graphs are determined with Hungarian algorithm to connect the loaded initial trap positions (blue circles) and empty target sites (red dots). The success rate was measured 35 % for 37 atoms.
Fig. 2
Fig. 2 Weighted-GS simulation of a defect-free array formation from an 11 by 11 square lattice. Optical tweezers for 58 randomly chosen atom locations are transported to around the center, while the the others are gradually turned off during the transport and turned back on at the end.
Fig. 3
Fig. 3 Monte-Carlo simulation of the induction GS algorithm: (a–c) trap-intensity transient minima are plotted, frame by frame, as a function of the step size (in unit of trap waist w0) for i = 5, f#=15, and Nz = 4 in a honeycomb array with 81 sites. The induction parameter ni (where Φ 0 ( k ) = Φ ( k n i )) is varied from (a) ni = −∞ (random initial phase), (b) ni = −3, and (c) ni = −1. Gray dots are individual results, red dots are averages, black dashed lines are numerical fits to C × exp ( x 2 / 2 w 0 2 ) with (a) C = 0.39, (b) C = 0.87, and (c) C = 0.94. The colored areas represent achievable minimal step size when zero-padding parameter Nz is 2 (skyblue, ×2) and 4 (darkblue, ×4). (d) Average transient minima for each induction parameter ni, when the step size is 0.25w0, and 0.5w0 (extracted from blue and red dashed lines, respectively in (a)–(c)), where the error bar is standard deviation.
Fig. 4
Fig. 4 Aberration correction considering the SLM pixel crosstalk. (a) Accumulated fluorescence images (5000 images) of atoms captured in 81 trap array, before and after the aberration correction. (b) Loading probability histograms of 81 trap array before and after the aberration correction.
Fig. 5
Fig. 5 Time sequence of tweezer-trap atom arrangement experiment, where the imaging and feedback processes are repeated Nf = 10 − 20 times as shown, and the entire sequence is repeated Nexp times at 0.5 Hz. Γ = 2π × 6 MHz denotes the spontaneous decay rate of 5P3/2.
Fig. 6
Fig. 6 Experimental demonstration of (a) the compaction rearrangement for various 2D arrays of initial 81 sites, and (b) the deterministic loading from initial 96 square lattice to alphabet letters. All the results were acquired by the same algorithm parameters, i.e. i = 5, Nz = 4, ni = −1, and f# = 15 (see Sec. 3 for details). The nearest distance is 3.7 μm for all the arrays.
Fig. 7
Fig. 7 Atom loading probability improved by feedback compaction to a honeycomb lattice from an initial 8 by 8 square lattice. (a) Individual loading probability is improved as the number of feedback Nf increases from 0 to 9, where the site number in the x axis is given in the distance order from the origin of the array. (b) The accumulation probability is improved near to 0.98N as Nf increases.
Fig. 8
Fig. 8 (a) Monte-Carlo simulation for the trap intensity transient minima vs. step size (in unit of trap waist) for various algorithm modifications. Doted-lines are C exp ( x 2 / 2 w 0 2 ) with C = 0.39, 0.94, and 1 (theoretical limit) for black, blue, and red, respectively. Shaded areas represent extended accessibility of smaller step size when zero-padding multiplier Nz is applied. The errorbars represent standard deviation.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

E ( x , y ; t ) = 𝔽 𝕋 [ 𝒜 exp ( i Φ ( t 1 ) ) exp { i ( Φ ( t 2 ) Φ ( t 1 ) ) w ( t ) } ] .
E ( t ) = E ( t 0 ) + { E ( t 1 ) E ( t 0 ) } w ( t )
T i ( x α , y α ) = T i 1 ( x α , y α ) T i 1 ( x α , y α ) α / A ( x α , y α ) A ( x α , y α ) α ,
Φ ( k ) Φ ( k 1 ) > π & Φ ( k ) > 2 π
Φ ( k ) Φ ( k 1 ) < π & Φ ( k ) < 2 π ,

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