Abstract

Engineering light-matter interaction using cold atomic arrays is one of the central topics in modern optics. Here we have demonstrated the capability of two-dimensional asymmetric cold atomic arrays as microscopic metasurfaces for controlling polarization states of light. The designed linear polarizer can lead to an extinction ratio over 20dB as well as a high transmittance over 0.8 for the permitted polarization at zero detuning. For detuned driving light, changing lattice constants can also achieve high performance linear polarizers. We have also accomplished a circular polarizer by manipulating the phases of transmitted light. A theoretical analysis based on Bloch theorem shows the underlying mechanism for this performance is actually attributed to cooperative effects in periodic lattices. Finally, we discuss in detail the effects of system size, lattice imperfection and nonzero driving light linewidth in practical implementation. The present study paves a way to design extremely miniaturized metasurfaces using cold atoms and other two-level systems, showing great potential in quantum information and quantum metrology sciences as well as the fundamental physics of light-matter interaction.

© 2017 Optical Society of America

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References

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2017 (5)

H. Kurosawa, B. Choi, Y. Sugimoto, and M. Iwanaga, “High-performance metasurface polarizers with extinction ratios exceeding 12000,” Opt. Express 25, 4446–4455 (2017).
[Crossref] [PubMed]

D. Kupriyanov, I. Sokolov, and M. Havey, “Mesoscopic coherence in light scattering from cold, optically dense and disordered atomic systems,” Phys. Rep. 6711–60 (2017).
[Crossref]

E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,” Phys. Rev. Lett. 118, 113601 (2017).
[Crossref] [PubMed]

B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
[Crossref] [PubMed]

M. Zhou, J. Liu, M. A. Kats, and Z. Yu, “Optical metasurface based on the resonant scattering in electronic transitions,” ACS Photonics 4, 1279–1285 (2017).
[Crossref]

2016 (14)

S. V. Kashanian, A. Eloy, W. Guerin, M. Lintz, M. Fouché, and R. Kaiser, “Noise spectroscopy with large clouds of cold atoms,” Phys. Rev. A 94, 043622 (2016).
[Crossref]

N. Goldman, J. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nature Physics 12, 639–645 (2016).
[Crossref]

T. Guo and C. Argyropoulos, “Broadband polarizers based on graphene metasurfaces,” Opt. Lett. 41, 5592–5595 (2016).
[Crossref] [PubMed]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array,” Phys. Rev. Lett. 116, 103602 (2016).
[Crossref] [PubMed]

N. Cherroret, D. Delande, and B. A. van Tiggelen, “Induced dipole-dipole interactions in light diffusion from point dipoles,” Phys. Rev. A 94, 012702 (2016).
[Crossref]

J. Ruostekoski and J. Javanainen, “Emergence of correlated optics in one-dimensional waveguides for classical and quantum atomic gases,” Phys. Rev. Lett. 117, 143602 (2016).
[Crossref] [PubMed]

J. Javanainen and J. Ruostekoski, “Light propagation beyond the mean-field theory of standard optics,” Opt. Express 24, 993–1001 (2016).
[Crossref] [PubMed]

N. Schilder, C. Sauvan, J.-P. Hugonin, S. Jennewein, Y. Sortais, A. Browaeys, and J.-J. Greffet, “Polaritonic modes in a dense cloud of cold atoms,” Phys. Rev. A 93, 063835 (2016).
[Crossref]

S.-M. Yoo and S. M. Paik, “Cooperative optical response of 2D dense lattices with strongly correlated dipoles,” Opt. Express 24, 2156–2165 (2016).
[Crossref] [PubMed]

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. LukâǍŹyanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
[Crossref] [PubMed]

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[Crossref] [PubMed]

H. Labuhn, D. Barredo, S. Ravets, S. De Lééleuc, 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] [PubMed]

D. Barredo, S. de Lééleuc, 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]

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Physics Reports 634, 1–72 (2016).
[Crossref]

2015 (5)

G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nature Nanotechnology 10, 308–312 (2015).
[Crossref]

T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
[Crossref]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnology 10, 937–943 (2015).
[Crossref] [PubMed]

B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds, and C. A. Regal, “Rapid production of uniformly filled arrays of neutral atoms,” Phys. Rev. Lett. 115, 073003 (2015).
[Crossref] [PubMed]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Cooperative ordering in lattices of interacting two-level dipoles,” Phys. Rev. A 92, 063822 (2015).
[Crossref]

2014 (4)

C. Wu, N. Arju, G. Kelp, J. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances,” Nature Communications 5, 3892 (2014).
[Crossref] [PubMed]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
[Crossref] [PubMed]

P. R. West, J. L. Stewart, A. V. Kildishev, V. M. Shalaev, V. V. Shkunov, F. Strohkendl, Y. A. Zakharenkov, R. K. Dodds, and R. Byren, “All-dielectric subwavelength metasurface focusing lens,” Opt. Express 22, 26212–26221 (2014).
[Crossref] [PubMed]

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).

2013 (2)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, “Long-range interacting many-body systems with alkaline-earth-metal atoms,” Phys. Rev. Lett. 110, 143602 (2013).
[Crossref] [PubMed]

2012 (2)

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
[Crossref]

S. D. Jenkins and J. Ruostekoski, “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

2011 (2)

C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

2008 (3)

A. Gero Akkermans and R. Kaiser, “Photon localization and Dicke superradiance in atomic gases,” Physical Review Letters 101, 103602 (2008).
[Crossref] [PubMed]

M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nature Physics 4, 924–927 (2008).
[Crossref]

I. Bloch, J. Dalibard, and W. Zwerger, “Many-body physics with ultracold gases,” Rev. Mod. Phys. 80, 885 (2008).
[Crossref]

2005 (1)

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

2003 (1)

D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
[Crossref]

2000 (1)

G. Labeyrie, C. Müller, D. Wiersma, C. Miniatura, and R. Kaiser, “Observation of coherent backscattering of light by cold atoms,” Journal of Optics B: Quantum and Semiclassical Optics 2, 672 (2000).
[Crossref]

1999 (2)

M. v. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313 (1999).
[Crossref]

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116 (1999).
[Crossref]

1951 (1)

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys. 23, 287 (1951).
[Crossref]

Adams, C. S.

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array,” Phys. Rev. Lett. 116, 103602 (2016).
[Crossref] [PubMed]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Cooperative ordering in lattices of interacting two-level dipoles,” Phys. Rev. A 92, 063822 (2015).
[Crossref]

Ahufinger, V.

M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems (Oxford University, 2012).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref] [PubMed]

Akkermans, A. Gero

A. Gero Akkermans and R. Kaiser, “Photon localization and Dicke superradiance in atomic gases,” Physical Review Letters 101, 103602 (2008).
[Crossref] [PubMed]

Aljunid, S. A.

M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nature Physics 4, 924–927 (2008).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnology 10, 937–943 (2015).
[Crossref] [PubMed]

Argyropoulos, C.

Arju, N.

C. Wu, N. Arju, G. Kelp, J. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances,” Nature Communications 5, 3892 (2014).
[Crossref] [PubMed]

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnology 10, 937–943 (2015).
[Crossref] [PubMed]

Barredo, D.

H. Labuhn, D. Barredo, S. Ravets, S. De Lééleuc, 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] [PubMed]

D. Barredo, S. de Lééleuc, 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]

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).

Belov, P. A.

S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Physics Reports 634, 1–72 (2016).
[Crossref]

Bettles, R. J.

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array,” Phys. Rev. Lett. 116, 103602 (2016).
[Crossref] [PubMed]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Cooperative ordering in lattices of interacting two-level dipoles,” Phys. Rev. A 92, 063822 (2015).
[Crossref]

Bidel, Y.

D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
[Crossref]

Bloch, I.

C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
[Crossref] [PubMed]

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T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
[Crossref]

Liu, J.

M. Zhou, J. Liu, M. A. Kats, and Z. Yu, “Optical metasurface based on the resonant scattering in electronic transitions,” ACS Photonics 4, 1279–1285 (2017).
[Crossref]

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B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds, and C. A. Regal, “Rapid production of uniformly filled arrays of neutral atoms,” Phys. Rev. Lett. 115, 073003 (2015).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. LukâǍŹyanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
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H. Labuhn, D. Barredo, S. Ravets, S. De Lééleuc, 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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D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. LukâǍŹyanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
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B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nature Nanotechnology 10, 308–312 (2015).
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D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
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G. Labeyrie, C. Müller, D. Wiersma, C. Miniatura, and R. Kaiser, “Observation of coherent backscattering of light by cold atoms,” Journal of Optics B: Quantum and Semiclassical Optics 2, 672 (2000).
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B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, “Long-range interacting many-body systems with alkaline-earth-metal atoms,” Phys. Rev. Lett. 110, 143602 (2013).
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H. Labuhn, D. Barredo, S. Ravets, S. De Lééleuc, 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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B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds, and C. A. Regal, “Rapid production of uniformly filled arrays of neutral atoms,” Phys. Rev. Lett. 115, 073003 (2015).
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B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds, and C. A. Regal, “Rapid production of uniformly filled arrays of neutral atoms,” Phys. Rev. Lett. 115, 073003 (2015).
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B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, “Long-range interacting many-body systems with alkaline-earth-metal atoms,” Phys. Rev. Lett. 110, 143602 (2013).
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E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,” Phys. Rev. Lett. 118, 113601 (2017).
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Shvets, G.

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B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
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D. Kupriyanov, I. Sokolov, and M. Havey, “Mesoscopic coherence in light scattering from cold, optically dense and disordered atomic systems,” Phys. Rep. 6711–60 (2017).
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N. Schilder, C. Sauvan, J.-P. Hugonin, S. Jennewein, Y. Sortais, A. Browaeys, and J.-J. Greffet, “Polaritonic modes in a dense cloud of cold atoms,” Phys. Rev. A 93, 063835 (2016).
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S. B. Glybovski, S. A. Tretyakov, P. A. Belov, Y. S. Kivshar, and C. R. Simovski, “Metasurfaces: From microwaves to visible,” Physics Reports 634, 1–72 (2016).
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C. Wu, N. Arju, G. Kelp, J. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances,” Nature Communications 5, 3892 (2014).
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B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
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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).

Wang, G.-M.

T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
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C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
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Wiersma, D.

G. Labeyrie, C. Müller, D. Wiersma, C. Miniatura, and R. Kaiser, “Observation of coherent backscattering of light by cold atoms,” Journal of Optics B: Quantum and Semiclassical Optics 2, 672 (2000).
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E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,” Phys. Rev. Lett. 118, 113601 (2017).
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D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
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T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
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E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,” Phys. Rev. Lett. 118, 113601 (2017).
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Yu, D.

B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, “Long-range interacting many-body systems with alkaline-earth-metal atoms,” Phys. Rev. Lett. 110, 143602 (2013).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
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M. Zhou, J. Liu, M. A. Kats, and Z. Yu, “Optical metasurface based on the resonant scattering in electronic transitions,” ACS Photonics 4, 1279–1285 (2017).
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T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nature Nanotechnology 10, 308–312 (2015).
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M. Zhou, J. Liu, M. A. Kats, and Z. Yu, “Optical metasurface based on the resonant scattering in electronic transitions,” ACS Photonics 4, 1279–1285 (2017).
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B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
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T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
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N. Goldman, J. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nature Physics 12, 639–645 (2016).
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ACS Photonics (1)

M. Zhou, J. Liu, M. A. Kats, and Z. Yu, “Optical metasurface based on the resonant scattering in electronic transitions,” ACS Photonics 4, 1279–1285 (2017).
[Crossref]

IEEE Trans. Antennas and Propagation (1)

T. Cai, G.-M. Wang, X.-F. Zhang, J.-G. Liang, Y.-Q. Zhuang, D. Liu, and H.-X. Xu, “Ultra-thin polarization beam splitter using 2-D transmissive phase gradient metasurface,” IEEE Trans. Antennas and Propagation 63, 5629–5636 (2015).
[Crossref]

Journal of Optics B: Quantum and Semiclassical Optics (1)

G. Labeyrie, C. Müller, D. Wiersma, C. Miniatura, and R. Kaiser, “Observation of coherent backscattering of light by cold atoms,” Journal of Optics B: Quantum and Semiclassical Optics 2, 672 (2000).
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Nature (2)

H. Labuhn, D. Barredo, S. Ravets, S. De Lééleuc, 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] [PubMed]

C. Weitenberg, M. Endres, J. F. Sherson, M. Cheneau, P. Schauss, T. Fukuhara, I. Bloch, and S. Kuhr, “Single-spin addressing in an atomic Mott insulator,” Nature 471, 319–324 (2011).
[Crossref] [PubMed]

Nature Communications (1)

C. Wu, N. Arju, G. Kelp, J. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared Fano resonances,” Nature Communications 5, 3892 (2014).
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Nature Materials (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
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Nature Nanotechnology (2)

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nature Nanotechnology 10, 937–943 (2015).
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G. Zheng, H. Mühlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nature Nanotechnology 10, 308–312 (2015).
[Crossref]

Nature Physics (3)

M. K. Tey, Z. Chen, S. A. Aljunid, B. Chng, F. Huber, G. Maslennikov, and C. Kurtsiefer, “Strong interaction between light and a single trapped atom without the need for a cavity,” Nature Physics 4, 924–927 (2008).
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I. Bloch, “Ultracold quantum gases in optical lattices,” Nature Physics 1, 23–30 (2005).
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N. Goldman, J. Budich, and P. Zoller, “Topological quantum matter with ultracold gases in optical lattices,” Nature Physics 12, 639–645 (2016).
[Crossref]

New J. Phys. (1)

L. Chomaz, L. Corman, T. Yefsah, R. Desbuquois, and J. Dalibard, “Absorption imaging of a quasi-two-dimensional gas: a multiple scattering analysis,” New J. Phys. 14, 055001 (2012).
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Opt. Express (4)

Opt. Lett. (1)

Phil. Trans. R. Soc. A (1)

B. A. Slovick, Y. Zhou, Z. G. Yu, I. I. Kravchenko, D. P. Briggs, P. Moitra, S. Krishnamurthy, and J. Valentine, “Metasurface polarization splitter,” Phil. Trans. R. Soc. A 375, 20160072 (2017).
[Crossref] [PubMed]

Phys. Rep. (1)

D. Kupriyanov, I. Sokolov, and M. Havey, “Mesoscopic coherence in light scattering from cold, optically dense and disordered atomic systems,” Phys. Rep. 6711–60 (2017).
[Crossref]

Phys. Rev. A (5)

N. Schilder, C. Sauvan, J.-P. Hugonin, S. Jennewein, Y. Sortais, A. Browaeys, and J.-J. Greffet, “Polaritonic modes in a dense cloud of cold atoms,” Phys. Rev. A 93, 063835 (2016).
[Crossref]

S. D. Jenkins and J. Ruostekoski, “Controlled manipulation of light by cooperative response of atoms in an optical lattice,” Phys. Rev. A 86, 031602 (2012).
[Crossref]

N. Cherroret, D. Delande, and B. A. van Tiggelen, “Induced dipole-dipole interactions in light diffusion from point dipoles,” Phys. Rev. A 94, 012702 (2016).
[Crossref]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Cooperative ordering in lattices of interacting two-level dipoles,” Phys. Rev. A 92, 063822 (2015).
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S. V. Kashanian, A. Eloy, W. Guerin, M. Lintz, M. Fouché, and R. Kaiser, “Noise spectroscopy with large clouds of cold atoms,” Phys. Rev. A 94, 043622 (2016).
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Phys. Rev. Lett. (7)

H. Katori, T. Ido, Y. Isoya, and M. Kuwata-Gonokami, “Magneto-optical trapping and cooling of strontium atoms down to the photon recoil temperature,” Phys. Rev. Lett. 82, 1116 (1999).
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B. Olmos, D. Yu, Y. Singh, F. Schreck, K. Bongs, and I. Lesanovsky, “Long-range interacting many-body systems with alkaline-earth-metal atoms,” Phys. Rev. Lett. 110, 143602 (2013).
[Crossref] [PubMed]

J. Ruostekoski and J. Javanainen, “Emergence of correlated optics in one-dimensional waveguides for classical and quantum atomic gases,” Phys. Rev. Lett. 117, 143602 (2016).
[Crossref] [PubMed]

R. J. Bettles, S. A. Gardiner, and C. S. Adams, “Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array,” Phys. Rev. Lett. 116, 103602 (2016).
[Crossref] [PubMed]

E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,” Phys. Rev. Lett. 118, 113601 (2017).
[Crossref] [PubMed]

B. J. Lester, N. Luick, A. M. Kaufman, C. M. Reynolds, and C. A. Regal, “Rapid production of uniformly filled arrays of neutral atoms,” Phys. Rev. Lett. 115, 073003 (2015).
[Crossref] [PubMed]

N. V. Corzo, B. Gouraud, A. Chandra, A. Goban, A. S. Sheremet, D. V. Kupriyanov, and J. Laurat, “Large Bragg reflection from one-dimensional chains of trapped atoms near a nanoscale waveguide,” Phys. Rev. Lett. 117, 133603 (2016).
[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).

Physica B: Condensed Matter (1)

D. Wilkowski, Y. Bidel, T. Chaneliere, R. Kaiser, B. Klappauf, G. Labeyrie, C. Müller, and C. Miniatura, “Light transport in cold atoms: the fate of coherent backscattering in the weak localization regime,” Physica B: Condensed Matter 328, 157–162 (2003).
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Physical Review Letters (1)

A. Gero Akkermans and R. Kaiser, “Photon localization and Dicke superradiance in atomic gases,” Physical Review Letters 101, 103602 (2008).
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Physics Reports (1)

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Figures (11)

Fig. 1
Fig. 1 (a) Configuration of the present 2D periodic atomic lattice located in xy plane at z = 0. The lattice is set to be rectangular with an asymmetric lattice structure in which lattice constants along x-axis and y-axis are ax and ay respectively. The normally incident light propagates along z-axis with a wavenumber kz. (b) A typical measuring method for collecting transmitted waves which is simulated in this paper. A lens is put in the downstream of the atomic arrays and a imaging screen in the far-field is positioned in the focus of the lens.
Fig. 2
Fig. 2 Transmission for different lattice constants at detuning Δ = 0.(a) Tx, the transmittance for x-polarized light. (b) Ty, the transmittance for y-polarized light.
Fig. 3
Fig. 3 Extinction ratio defined as ER = 10 log10(Tx/Ty) in units of decibel (dB), which quantifies the efficiency of linear polarization conversion.
Fig. 4
Fig. 4 Electric field intensity distribution at Δ = 0 and z = 0 for the optimal lattice structure ax/λ0 = 0.78 and ay/λ0 = 0.94 in logarithmic scale. (a) log10 Ix, electric field intensity distribution for x-polarized light. (b) log10 Iy, electric field intensity distribution for y-polarized light. These figures are extracted from the center of a larger simulation zone to avoid edge effects.
Fig. 5
Fig. 5 Transmittance spectra of x-polarized light and y-polarized light for the optimal lattice structure ax/λ0 = 0.78 and ay/λ0 = 0.94. The result from independent scattering approximation (ISA) irrelevant with polarization is also shown in dashed line.
Fig. 6
Fig. 6 Optimal lattice constants for different incident light detunings Δ to achieve linear polarization conversion. The obtained lattice constants and extinction ratio at each detuning are circumscribed with a dashed-lined rectangular box for readability.
Fig. 7
Fig. 7 Degree of circular polarization (DCP) calculated for different lattice constants. When the absolute value of DCP is closer to 1, a higher degree of circular polarization is achieved.
Fig. 8
Fig. 8 (a) Transmittance and (b) phase difference spectra for ax/λ0 = 0.165 and ay/λ0 = 0.375.
Fig. 9
Fig. 9 Effect of system size on the performance of atomic metasurfaces for (a) linear polarizer with the optimal lattice structure ax/λ0 = 0.78 and ay/λ0 = 0.94 (b) circular polarizer with the optimal lattice structure ax/λ0 = 0.165 and ay/λ0 = 0.375. Here Nx = Ny.
Fig. 10
Fig. 10 Effect of positional disorder on the performance of atomic metasurfaces for (a) linear polarizer with the optimal lattice structure ax/λ0 = 0.78 and ay/λ0 = 0.94 (b) circular polarizer with the optimal lattice structure ax/λ0 = 0.165 and ay/λ0 = 0.375.
Fig. 11
Fig. 11 Spectral performance parameters of the atomic metasurfaces. (a) ER, for linear polarizer with the optimal lattice structure ax/λ0 = 0.78 and ay/λ0 = 0.94 (b) DCP, for circular polarizer with the optimal lattice structure ax/λ0 = 0.165 and ay/λ0 = 0.375.

Equations (16)

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α ( ω ) = 6 π c 3 ω 3 γ / 2 ω ω 0 + i γ / 2
p j ( ω ) = α ( ω ) [ E i n c ( r j ) + ω 2 c 2 i = 1 , i j N G 0 ( ω , r j , r i ) p i ( ω ) ]
G 0 ( ω , r j , r i ) = exp ( i k r ) 4 π r [ ( i k r 1 k 2 r 2 + 1 ) I + ( 3 i k r + 3 k 2 r 2 1 ) r ^ r ^ ]
p e = α ( ω ) [ E i n c ( r j ) + ω 2 c 2 i = 1 , i j N G 0 ( ω , r j , r i ) p e ]
p e = E i n c ( 0 ) a ( ω ) 1 I k 2 g ( a x . a y )
g ( a x , a y ) = m = 0 N x n = 0 N y G 0 ( 0 , m a x e ^ x + n a y e ^ y )
α e f f ( ω , a x , a y ) = 6 π c 3 ω 3 γ / 2 [ Δ I Δ ( a x , a y ) ] + i [ γ I γ ( a x , a y ) ] / 2
  ( a x , a y ) = 3 π γ k Re [ g ( a x , a y ) ]
γ ( a x , a y ) = 6 π γ k Im [ g ( a x , a y ) ]
E ( r ) = E i n c ( r ) + ω 2 c 2 i = 1 N G 0 ( ω , r , r i ) p i ( ω )
t β = 1 + i k 2 E 0 L x L y i = 1 N p i   , β exp ( i k z i )
T β = | t β | 2
E R = 10 log 10 ( T x T y )
T i n d ( ω ) = exp [ N σ ( ω ) A ]
Δ Φ = Φ ( t y ) Φ ( t x )
D C P = S 3 S 0 = 2 Im [ E t , x E t , y * ] | E t , x | 2 + | E t , y | 2

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