Abstract

We propose and demonstrate three-dimensional rearrangements of single atoms. In experiments performed with single 87Rb atoms in optical microtraps actively controlled by a spatial light modulator, we demonstrate various dynamic rearrangements of up to N = 9 atoms including rotation, 2D vacancy filling, guiding, compactification, and 3D shuffling. With the capability of a phase-only Fourier mask to generate arbitrary shapes of the holographic microtraps, it was possible to place single atoms at arbitrary geometries of a few μm size and even continuously reconfigure them by conveying each atom. For this purpose, we loaded a series of computer-generated phase masks in the full frame rate of 60 Hz of the spatial light modulator, so the animation of phase mask transformed the holographic microtraps in real time, driving each atom along the assigned trajectory. Possible applications of this method of transformation of single atoms include preparation of scalable quantum platforms for quantum computation, quantum simulation, and quantum many-body physics.

© 2016 Optical Society of America

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References

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  1. J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
    [Crossref]
  2. S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
    [Crossref] [PubMed]
  3. J. I. Cirac and P. Zoller, “A scalable quantum computer with ions in an array of microtraps,” Nature 404, 579–581 (2000).
    [Crossref] [PubMed]
  4. S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B 21, 1889–1894 (2004).
    [Crossref]
  5. F. K. Fatemi, M. Bashkansky, and Z. Dutton, “Dynamic high-speed spatial manipulation of cold atoms using acousto-optic and spatial light modulation,” Opt. Express 15, 3589–3596 (2007).
    [Crossref] [PubMed]
  6. X. He, P. Xu, J. Wang, and M. Zhan, “Rotating single atoms in a ring lattice generated by a spatial light modulator,” Opt. Express 17, 21007–21014 (2009).
    [Crossref] [PubMed]
  7. 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).
  8. J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
    [Crossref]
  9. S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
    [Crossref] [PubMed]
  10. M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
    [Crossref] [PubMed]
  11. Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
    [Crossref]
  12. M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
    [Crossref]
  13. N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
    [Crossref] [PubMed]
  14. 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] [PubMed]
  15. I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
    [Crossref]
  16. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
    [Crossref] [PubMed]
  17. I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
    [Crossref]
  18. M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
    [Crossref]
  19. H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [Crossref]
  20. T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
    [Crossref]
  21. D. McGloin, G. C. Spalding, H. Melville, W. Sibbett, and K. Dholakia, “Applications of spatial light modulators in atom optics,” Opt. Express 11, 158–166 (2003).
    [Crossref] [PubMed]
  22. H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833
  23. A. Jechow, E. W. Streed, B. G. Norton, M. J. Petrasiunas, and D. Kielpinski, “Wavelength-scale imaging of trapped ions using a phase Fresnel lens,” Opt. Lett. 36, 1371–1373 (2011).
    [Crossref] [PubMed]
  24. R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
    [Crossref]
  25. 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, 21010–21026 (2013).
    [Crossref] [PubMed]

2015 (1)

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] [PubMed]

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).

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

2013 (2)

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, 21010–21026 (2013).
[Crossref] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

2011 (2)

A. Jechow, E. W. Streed, B. G. Norton, M. J. Petrasiunas, and D. Kielpinski, “Wavelength-scale imaging of trapped ions using a phase Fresnel lens,” Opt. Lett. 36, 1371–1373 (2011).
[Crossref] [PubMed]

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

2010 (1)

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

2009 (1)

2007 (2)

F. K. Fatemi, M. Bashkansky, and Z. Dutton, “Dynamic high-speed spatial manipulation of cold atoms using acousto-optic and spatial light modulation,” Opt. Express 15, 3589–3596 (2007).
[Crossref] [PubMed]

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

2006 (1)

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

2005 (1)

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[Crossref]

2004 (1)

2003 (2)

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

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

2002 (2)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
[Crossref] [PubMed]

2001 (1)

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

2000 (2)

J. I. Cirac and P. Zoller, “A scalable quantum computer with ions in an array of microtraps,” Nature 404, 579–581 (2000).
[Crossref] [PubMed]

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
[Crossref]

1986 (1)

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

1978 (1)

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

1971 (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Ahn, J.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Alt, W.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Andersen, M. F.

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Ashhab, S.

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
[Crossref]

Ashkin, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

Barredo, D.

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).

Bashkansky, M.

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).

Bergamini, S.

Beugnon, J.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Birkl, G.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

Bjorkholm, J. E.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

Bloch, I.

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[Crossref]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

Bowman, R. W.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Browaeys, 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).

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B 21, 1889–1894 (2004).
[Crossref]

Buluta, I.

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
[Crossref]

Cable, A.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Carberry, D. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[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] [PubMed]

Chu, S.

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Cirac, J. I.

J. I. Cirac and P. Zoller, “A scalable quantum computer with ions in an array of microtraps,” Nature 404, 579–581 (2000).
[Crossref] [PubMed]

Dammann, H.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Darquie, B.

Dholakia, K.

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

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Dotsenko, I.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Dutton, Z.

Fahrbach, F. O.

Fatemi, F. K.

Förster, L.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Freeman, R. R.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

Gaëtan, A

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Gibson, G. M.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Gomer, V.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Görtler, K.

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Grangier, P.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

S. Bergamini, B. Darquie, M. Jones, L. Jacubowiez, A. Browaeys, and P. Grangier, “Holographic generation of microtrap arrays for single atoms by use of a programmable phase modulator,” J. Opt. Soc. Am. B 21, 1889–1894 (2004).
[Crossref]

N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
[Crossref] [PubMed]

Greiner, M.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

Grieve, J. A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Grünzweig, T.

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

Hänsch, T. W.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

He, X.

Helmchen, F.

Hilliard, A.

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

Huisken, J.

Isenhower, L.

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] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Jacubowiez, L.

Jechow, A.

Jo, H.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Jones, M.

Jones, M. P. A.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Khudaverdyan, M.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Kielpinski, D.

Kim, H.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Kruse, J.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

Kuhr, S.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Labuhn, H.

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).

Lahaye, T.

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).

Lance, A. M.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Lee, H.-g.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Lee, W.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Li, G.

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Lichtman, 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] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Linnenberger, A.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Maller, K.

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] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Mandel, O.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

Marion, H.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

McGloin, D.

McGovern, M.

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

Melville, H.

Meschede, D.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Messin, G.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Miles, M. J.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Miroshnychenko, Y.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Müller, M.

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Nogrette, F.

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).

Nori, F.

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
[Crossref]

Norton, B. G.

Padgett, M. J.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Pearson, D. B.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

Petrasiunas, M. J.

Phillips, D. B.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Piotrowicz, M. J.

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] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Rauschenbeutel, A.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Ravets, S.

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).

Reymond, G.

N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
[Crossref] [PubMed]

Rom, T.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

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] [PubMed]

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Schlosser, M.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

Schlosser, N.

N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
[Crossref] [PubMed]

Schmid, B.

Schrader, D.

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

Serati, S.

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

Sibbett, W.

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

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Song, Y.

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Sortais, Y. R. P.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

Spalding, G. C.

Streed, E. W.

Tichelmann, S.

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

Tuchendler, C.

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

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.

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Wang, J.

Widera, A.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

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] [PubMed]

Xu, P.

Zhan, M.

Zhang, S.

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Zoller, P.

J. I. Cirac and P. Zoller, “A scalable quantum computer with ions in an array of microtraps,” Nature 404, 579–581 (2000).
[Crossref] [PubMed]

Comput. Phys. Commun. (1)

R. W. Bowman, G. M. Gibson, A. Linnenberger, D. B. Phillips, J. A. Grieve, D. M. Carberry, S. Serati, M. J. Miles, and M. J. Padgett, “Red Tweezers: Fast, customisable hologram generation for optical tweezers,” Comput. Phys. Commun. 185, 268–273 (2014).
[Crossref]

J. Opt. Soc. Am. B (1)

Nat. Phys. (3)

J. Beugnon, C. Tuchendler, H. Marion, A Gaëtan, Y. Miroshnychenko, Y. R. P. Sortais, A. M. Lance, M. P. A. Jones, G. Messin, A. Browaeys, and P. Grangier, “Two-dimensional transport and transfer of a single atomic qubit in optical tweezers,” Nat. Phys. 3, 696–699 (2007).
[Crossref]

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1, 23–30 (2005).
[Crossref]

T. Grünzweig, A. Hilliard, M. McGovern, and M. F. Andersen, “Near-deterministic preparation of a single atom in an optical microtrap,” Nat. Phys. 6, 951–954 (2010).
[Crossref]

Nature (3)

J. I. Cirac and P. Zoller, “A scalable quantum computer with ions in an array of microtraps,” Nature 404, 579–581 (2000).
[Crossref] [PubMed]

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hänsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937–940 (2003).
[Crossref] [PubMed]

Y. Miroshnychenko, W. Alt, I. Dotsenko, L. Förster, M. Khudaverdyan, D. Meschede, D. Schrader, and A. Rauschenbeutel, “An atom-sorting machine,” Nature 442, 151 (2006).
[Crossref]

Opt. Commun. (1)

H. Dammann and K. Görtler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

M. J. Piotrowicz, M. Lichtman, K. Maller, G. Li, S. Zhang, L. Isenhower, and M. Saffman, “Two-dimensional lattice of blue-detuned atom traps using a projected Gaussian beam array,” Phys. Rev. A 88, 013420 (2013).
[Crossref]

Phys. Rev. Lett. (4)

N. Schlosser, G. Reymond, and P. Grangier, “Collisional blockade in microscopic optical dipole traps,” Phys. Rev. Lett. 89, 023005 (2002).
[Crossref] [PubMed]

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] [PubMed]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, and D. B. Pearson, “Observation of focusing of neutral atoms by the dipole forces of resonance-radiation pressure,” Phys. Rev. Lett. 41, 1361–1364 (1978).
[Crossref]

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[Crossref] [PubMed]

Phys. Rev. X (1)

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).

Quant. Inf. Proc. (1)

M. Schlosser, S. Tichelmann, J. Kruse, and G. Birkl, “Scalable architecture for quantum information processing with atoms in optical micro-structures,” Quant. Inf. Proc. 10, 907–924 (2011).
[Crossref]

Rep. Prog. Phys. (1)

I. Buluta, S. Ashhab, and F. Nori, “Natural and artificial atoms for quantum computation,” Rep. Prog. Phys. 74, 104401 (2000).
[Crossref]

Science (2)

S. Kuhr, W. Alt, D. Schrader, M. Müller, V. Gomer, and D. Meschede, “Deterministic delivery of a single atom,” Science 293, 278 (2001).
[Crossref] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, “Creation and manipulation of three-dimensional optically trapped structures,” Science 296, 1101–1103 (2002).
[Crossref] [PubMed]

Other (1)

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, “In situ single-atom array synthesis by dynamic holographic optical tweezers,” http://arxiv.org/abs/1601.03833

Supplementary Material (8)

NameDescription
» Visualization 1: MP4 (284 KB)      Fig. 3(a) Array rotation
» Visualization 2: MP4 (287 KB)      Fig. 3(b) Vacancy filling
» Visualization 3: MP4 (645 KB)      Fig. 3(c) Worm running
» Visualization 4: MP4 (418 KB)      Fig. 3(d) Fall to the right: case 1
» Visualization 5: MP4 (419 KB)      Fig. 3(e) Fall to the right: case 2
» Visualization 6: MP4 (419 KB)      Fig. 3(f) Fall to the right: case 3
» Visualization 7: MP4 (78 KB)      Fig. 4(b) Accumulated-event video
» Visualization 8: MP4 (168 KB)      Fig. 4(b) Single-event video

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Figures (5)

Fig. 1
Fig. 1 (a) Transverse displacement of focal spots. (b) Axial displacement. (c) Phase pattern synthesis.
Fig. 2
Fig. 2 Schematic illustration of the experimental setup. Optical microtraps were programmed with the LCOS-SLM to capture single atoms from the pre-cooled 87Rb ensemble in the MOT. The information of the trapped single-atom configuration obtained with the EMCCD was sent back to the SLM computer for the feedback control.
Fig. 3
Fig. 3 Selected results of demonstration. (a) Rotation of a 3-by-3 array as a collective control. (b) 2D vacancy filling and (c) Worm running as individual atom controls. (d–f) Rightward alignment as feedback controls of atom arrays. The leftmost column presents the schematic diagram of each operation scenario. In each column, the initial and in-between photos are followed by the final photos (see Visualization 1, Visualization 2, Visualization 3, Visualization 4, Visualization 5, and Visualization 6).
Fig. 4
Fig. 4 (a) Trapping and imaging of a 3D single-atom array, where the image plane was shifted by translating the EMCCD. Each image corresponded to the EMCCD position at z = −10, −5, 0, 5, 10 mm and was accumulated from 100 single-event images that were captured right after the atoms were trapped in each acquisition. (b) Individual transport of single atoms in 3D, where each demonstration spanned 90 SLM frames and each step of atom moving was an equal division of the entire path. 370-time accumulated sequential images (the upper panel, see Visualization 7) and selected single-event sequential images (the lower panel, see Visualization 8) are displayed. The lattice constant of the 2D array was d = 4.5 μm and the depth of the axial travels for the both atoms were 4 μm.
Fig. 5
Fig. 5 (a) Single-atom transport efficiency vs. the step distance in a 40-step (41 frames) transport operation, where the values for moving in positive and negative directions are drawn with dashed and dash-dot black lines, respectively, and the total average with the blue line with ‘star’ marks. The given transport (only) efficiency is the actually measured probability divided by the probability without moving. (b) Single-atom transport efficiency vs. the travel distance (with a fixed step distance of 250 nm) for various frame refresh rates and directions. (c), (d) The single-step loss vs. the step distance and travel distance, calculated from the main data in (a) and (b), respectively.

Equations (3)

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

( Δ x , Δ y , Δ z ) = ( k X f o k , k Y f o k , f o 2 f F )
ϕ ( X , Y ) = m o d ( k X X + k Y Y + k 2 f F ( X 2 + Y 2 ) + π , 2 π ) ,
ϕ mixed ( i , j ) = ϕ S ( i , j ) ( i , j ) .

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