Photon-photon interactions in Rydberg-atom arrays

Lida Zhang; Valentin Walther; Klaus Mølmer; Thomas Pohl

doi:10.22331/q-2022-03-30-674

Photon-photon interactions in Rydberg-atom arrays

Lida Zhang¹, Valentin Walther^1,2, Klaus Mølmer¹, and Thomas Pohl¹

¹Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
²ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA

Published:	2022-03-30, volume 6, page 674
Eprint:	arXiv:2101.11375v3
Doi:	https://doi.org/10.22331/q-2022-03-30-674
Citation:	Quantum 6, 674 (2022).

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Abstract

We investigate the interaction of weak light fields with two-dimensional lattices of atoms with high lying atomic Rydberg states. This system features different interactions that act on disparate length scales, from zero-range defect scattering of atomic excitations and finite-range dipole exchange processes to long-range Rydberg-state interactions, which span the entire array and can block multiple Rydberg excitations. Analyzing their interplay, we identify conditions that yield a nonlinear quantum mirror which coherently splits incident fields into correlated photon-pairs in a single transverse mode, while transmitting single photons unaffected. In particular, we find strong anti-bunching of the transmitted light with equal-time pair correlations that decrease exponentially with an increasing range of the Rydberg blockade. Such strong photon-photon interactions in the absence of photon losses open up promising avenues for the generation and manipulation of quantum light, and the exploration of many-body phenomena with interacting photons.

► BibTeX data

@article{Zhang2022photonphoton,
  doi = {10.22331/q-2022-03-30-674},
  url = {https://doi.org/10.22331/q-2022-03-30-674},
  title = {Photon-photon interactions in {R}ydberg-atom arrays},
  author = {Zhang, Lida and Walther, Valentin and M{\o{}}lmer, Klaus and Pohl, Thomas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {674},
  month = mar,
  year = {2022}
}

► References

[1] D. E. Chang, V. Vuletić, and M. D. Lukin, Nature Photonics 8, 685 (2014).
https://doi.org/10.1038/nphoton.2014.192

[2] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).
https://doi.org/10.1038/nature03804

[3] J. Volz, M. Scheucher, C. Junge, and A. Rauschenbeutel, Nature Photonics 8, 965 (2014).
https://doi.org/10.1038/nphoton.2014.253

[4] A. Reiserer and G. Rempe, Rev. Mod. Phys. 87, 1379 (2015).
https://doi.org/10.1103/RevModPhys.87.1379

[5] S. Welte, B. Hacker, S. Daiss, S. Ritter, and G. Rempe, Phys. Rev. X 8, 011018 (2018).
https://doi.org/10.1103/PhysRevX.8.011018

[6] D. O'Shea, C. Junge, J. Volz, and A. Rauschenbeutel, Phys. Rev. Lett. 111, 193601 (2013).
https://doi.org/10.1103/PhysRevLett.111.193601

[7] A. Goban, K. S. Choi, D. J. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. P. Stern, and H. J. Kimble, Phys. Rev. Lett. 109, 033603 (2012).
https://doi.org/10.1103/PhysRevLett.109.033603

[8] J. D. Thompson, T. G. Tiecke, N. P. de Leon, J. Feist, A. V. Akimov, M. Gullans, A. S. Zibrov, V. Vuletić, and M. D. Lukin, Science 340, 1202 (2013).
https://doi.org/10.1126/science.1237125

[9] T. G. Tiecke, J. D. Thompson, N. P. de Leon, L. R. Liu, V. Vuletić, and M. D. Lukin, Nature 508, 241 (2014).
https://doi.org/10.1038/nature13188

[10] J. Petersen, J. Volz, and A. Rauschenbeutel, Science 346, 67 (2014).
https://doi.org/10.1126/science.1257671

[11] P. Lodahl, S. Mahmoodian, and S. Stobbe, Rev. Mod. Phys. 87, 347 (2015).
https://doi.org/10.1103/RevModPhys.87.347

[12] D. E. Chang, J. S. Douglas, A. González-Tudela, C.-L. Hung, and H. J. Kimble, Rev. Mod. Phys. 90, 031002 (2018).
https://doi.org/10.1103/RevModPhys.90.031002

[13] M. Noaman, M. Langbecker, and P. Windpassinger, Opt. Lett. 43, 3925 (2018).
https://doi.org/10.1364/OL.43.003925

[14] S.-P. Yu, J. A. Muniz, C.-L. Hung, and H. J. Kimble, Proceedings of the National Academy of Sciences 116, 12743 (2019).
https://doi.org/10.1073/pnas.1822110116

[15] A. S. Prasad, J. Hinney, S. Mahmoodian, K. Hammerer, S. Rind, P. Schneeweiss, A. S. Sørensen, J. Volz, and A. Rauschenbeutel, Nature Photonics 14, 719 (2020).
https://doi.org/10.1038/s41566-020-0692-z

[16] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, Phys. Rev. Lett. 105, 193603 (2010).
https://doi.org/10.1103/PhysRevLett.105.193603

[17] T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, Nature 488, 57 (2012).
https://doi.org/10.1038/nature11361

[18] J. D. Thompson, T. L. Nicholson, Q.-Y. Liang, S. H. Cantu, A. V. Venkatramani, S. Choi, I. A. Fedorov, D. Viscor, T. Pohl, M. D. Lukin, and V. Vuletić, Nature 542, 206 (2017).
https://doi.org/10.1038/nature20823

[19] A. Paris-Mandoki, C. Braun, J. Kumlin, C. Tresp, I. Mirgorodskiy, F. Christaller, H. P. Büchler, and S. Hofferberth, Phys. Rev. X 7, 041010 (2017).
https://doi.org/10.1103/PhysRevX.7.041010

[20] C. Murray and T. Pohl, Advances In Atomic, Molecular, and Optical Physics, 65, 321 (2016).
https://doi.org/10.1016/bs.aamop.2016.04.005

[21] O. Firstenberg, C. S. Adams, and S. Hofferberth, J. Phys B 49, 152003 (2016).
https://doi.org/10.1088/0953-4075/49/15/152003

[22] S. Baur, D. Tiarks, G. Rempe, and S. Dürr, Phys. Rev. Lett. 112, 073901 (2014).
https://doi.org/10.1103/PhysRevLett.112.073901

[23] H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, Phys. Rev. Lett. 113, 053601 (2014).
https://doi.org/10.1103/PhysRevLett.113.053601

[24] D. Tiarks, S. Baur, K. Schneider, S. Dürr, and G. Rempe, Phys. Rev. Lett. 113, 053602 (2014).
https://doi.org/10.1103/PhysRevLett.113.053602

[25] D. Tiarks, S. Schmidt-Eberle, T. Stolz, G. Rempe, and S. Dürr, Nature Physics 15, 124 (2019).
https://doi.org/10.1038/s41567-018-0313-7

[26] A. V. Gorshkov, R. Nath, and T. Pohl, Phys. Rev. Lett. 110, 153601 (2013).
https://doi.org/10.1103/PhysRevLett.110.153601

[27] C. R. Murray, I. Mirgorodskiy, C. Tresp, C. Braun, A. Paris-Mandoki, A. V. Gorshkov, S. Hofferberth, and T. Pohl, Phys. Rev. Lett. 120, 113601 (2018).
https://doi.org/10.1103/PhysRevLett.120.113601

[28] C. R. Murray, A. V. Gorshkov, and T. Pohl, New Journal of Physics 18, 092001 (2016).
https://doi.org/10.1088/1367-2630/18/9/092001

[29] J. Otterbach, M. Moos, D. Muth, and M. Fleischhauer, Phys. Rev. Lett. 111, 113001 (2013).
https://doi.org/10.1103/PhysRevLett.111.113001

[30] E. Zeuthen, M. J. Gullans, M. F. Maghrebi, and A. V. Gorshkov, Phys. Rev. Lett. 119, 043602 (2017).
https://doi.org/10.1103/PhysRevLett.119.043602

[31] P. Bienias, J. Douglas, A. Paris-Mandoki, P. Titum, I. Mirgorodskiy, C. Tresp, E. Zeuthen, M. J. Gullans, M. Manzoni, S. Hofferberth, D. Chang, and A. V. Gorshkov, Phys. Rev. Research 2, 033049 (2020).
https://doi.org/10.1103/PhysRevResearch.2.033049

[32] G. Facchinetti, S. D. Jenkins, and J. Ruostekoski, Phys. Rev. Lett. 117, 243601 (2016).
https://doi.org/10.1103/PhysRevLett.117.243601

[33] J. Perczel, J. Borregaard, D. E. Chang, H. Pichler, S. F. Yelin, P. Zoller, and M. D. Lukin, Phys. Rev. Lett. 119, 023603 (2017).
https://doi.org/10.1103/PhysRevLett.119.023603

[34] R. J. Bettles, J. c. v. Minář, C. S. Adams, I. Lesanovsky, and B. Olmos, Phys. Rev. A 96, 041603 (2017).
https://doi.org/10.1103/PhysRevA.96.041603

[35] P.-O. Guimond, A. Grankin, D. V. Vasilyev, B. Vermersch, and P. Zoller, Phys. Rev. Lett. 122, 093601 (2019).
https://doi.org/10.1103/PhysRevLett.122.093601

[36] K. E. Ballantine and J. Ruostekoski, Phys. Rev. Lett. 125, 143604 (2020).
https://doi.org/10.1103/PhysRevLett.125.143604

[37] R. J. Bettles, S. A. Gardiner, and C. S. Adams, Phys. Rev. Lett. 116, 103602 (2016).
https://doi.org/10.1103/PhysRevLett.116.103602

[38] E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, Phys. Rev. Lett. 118, 113601 (2017).
https://doi.org/10.1103/PhysRevLett.118.113601

[39] J. Rui, D. Wei, A. Rubio-Abadal, S. Hollerith, J. Zeiher, D. M. Stamper-Kurn, C. Gross, and I. Bloch, Nature 583, 369 (2020).
https://doi.org/10.1038/s41586-020-2463-x

[40] A. Grankin, P. O. Guimond, D. V. Vasilyev, B. Vermersch, and P. Zoller, Phys. Rev. A 98, 043825 (2018).
https://doi.org/10.1103/PhysRevA.98.043825

[41] R. Bekenstein, I. Pikovski, H. Pichler, E. Shahmoon, S. F. Yelin, and M. D. Lukin, Nature Physics 16, 676 (2020).
https://doi.org/10.1038/s41567-020-0845-5

[42] A. Cidrim, T. S. do Espirito Santo, J. Schachenmayer, R. Kaiser, and R. Bachelard, Phys. Rev. Lett. 125, 073601 (2020).
https://doi.org/10.1103/PhysRevLett.125.073601

[43] L. A. Williamson, M. O. Borgh, and J. Ruostekoski, Phys. Rev. Lett. 125, 073602 (2020).
https://doi.org/10.1103/PhysRevLett.125.073602

[44] M. Moreno-Cardoner, D. Goncalves, and D. E. Chang, Phys. Rev. Lett. 127, 263602 (2021).
https://doi.org/10.1103/PhysRevLett.127.263602

[45] N. Henkel, R. Nath, and T. Pohl, Phys. Rev. Lett. 104, 195302 (2010).
https://doi.org/10.1103/PhysRevLett.104.195302

[46] J. Zeiher, P. Schauß, S. Hild, T. Macrì, I. Bloch, and C. Gross, Phys. Rev. X 5, 031015 (2015).
https://doi.org/10.1103/PhysRevX.5.031015

[47] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Phys. Rev. Lett. 85, 2208 (2000).
https://doi.org/10.1103/PhysRevLett.85.2208

[48] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 87, 037901 (2001).
https://doi.org/10.1103/PhysRevLett.87.037901

[49] M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010).
https://doi.org/10.1103/RevModPhys.82.2313

[50] C. S. Adams, J. D. Pritchard, and J. P. Shaffer, Journal of Physics B: Atomic, Molecular and Optical Physics 53, 012002 (2019).
https://doi.org/10.1088/1361-6455/ab52ef

[51] D. F. V. James, Phys. Rev. A 47, 1336 (1993).
https://doi.org/10.1103/PhysRevA.47.1336

[52] H. T. Dung, L. Knöll, and D.-G. Welsch, Phys. Rev. A 66, 063810 (2002).
https://doi.org/10.1103/PhysRevA.66.063810

[53] A. Asenjo-Garcia, J. D. Hood, D. E. Chang, and H. J. Kimble, Phys. Rev. A 95, 033818 (2017).
https://doi.org/10.1103/PhysRevA.95.033818

[54] H. Zoubi and H. Ritsch, Phys. Rev. A 83, 063831 (2011).
https://doi.org/10.1103/PhysRevA.83.063831

[55] R. T. Sutherland and F. Robicheaux, Phys. Rev. A 94, 013847 (2016).
https://doi.org/10.1103/PhysRevA.94.013847

[56] R. J. Bettles, S. A. Gardiner, and C. S. Adams, Phys. Rev. A 92, 063822 (2015).
https://doi.org/10.1103/PhysRevA.92.063822

[57] Y.-X. Zhang and K. Mølmer, Phys. Rev. Lett. 122, 203605 (2019).
https://doi.org/10.1103/PhysRevLett.122.203605

[58] A. Glicenstein, G. Ferioli, N. Šibalić, L. Brossard, I. Ferrier-Barbut, and A. Browaeys, Phys. Rev. Lett. 124, 253602 (2020).
https://doi.org/10.1103/PhysRevLett.124.253602

[59] A. Piñeiro Orioli and A. M. Rey, Phys. Rev. Lett. 123, 223601 (2019).
https://doi.org/10.1103/PhysRevLett.123.223601

[60] M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. 84, 5094 (2000).
https://doi.org/10.1103/PhysRevLett.84.5094

[61] E. Arimondo, Progress in Optics, 35, 257 (1996).
https://doi.org/10.1016/S0079-6638(08)70531-6

[62] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
https://doi.org/10.1103/RevModPhys.77.633

[63] M. T. Manzoni, M. Moreno-Cardoner, A. Asenjo-Garcia, J. V. Porto, A. V. Gorshkov, and D. E. Chang, New Journal of Physics 20, 083048 (2018).
https://doi.org/10.1088/1367-2630/aadb74

[64] C. R. Murray, and T. Pohl, Phys. Rev. X 7, 031007 (2017).
https://doi.org/10.1103/PhysRevX.7.031007

[65] K. Mølmer, Y. Castin, and J. Dalibard, J. Opt. Soc. Am. B 10, 524 (1993).
https://doi.org/10.1364/JOSAB.10.000524

[66] N. Stiesdal, H. Busche, K. Kleinbeck, J. Kumlin, M. G. Hansen, H. P. Büchler, and S. Hofferberth, Nature Communications 12, 4328 (2021).
https://doi.org/10.1038/s41467-021-24522-w

[67] A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
https://doi.org/10.1103/PhysRevLett.71.3095

[68] T. C. Ralph, I. Söllner, S. Mahmoodian, A. G. White, and P. Lohdal, Phys. Rev. Lett. 114, 173603 (1993).
https://doi.org/10.1103/PhysRevLett.114.173603

[69] D. Witthaut, M. D. Lukin, and A. S. Sørensen, EPL 97, 50007 (2015).
https://doi.org/10.1209/0295-5075/97/50007

[70] E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, ``Theory of cavity qed with 2d atomic arrays,'' (2020), arXiv:2006.01972.
https://doi.org/10.48550/arXiv.2006.01972
arXiv:arXiv:2006.01972

[71] R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołlodyński, Progress in Optics, 60, 345 (2015).
https://doi.org/10.1016/bs.po.2015.02.003

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[1] Roni Ben-Maimon, Yakov Solomons, Nir Davidson, Ofer Firstenberg, and Ephraim Shahmoon, "Quantum Interfaces with Multilayered Superwavelength Atomic Arrays", Physical Review Letters 135 3, 033601 (2025).

[2] Jonas von Milczewski, Kelly Werker Smith, and Susanne F. Yelin, "Directional quantum scattering transducer in cooperative Rydberg metasurfaces", Physical Review A 113 4, 043716 (2026).

[3] N. Fayard, I. Ferrier-Barbut, A. Browaeys, and J.-J. Greffet, "Optical control of collective states in one-dimensional ordered atomic chains beyond the linear regime", Physical Review A 108 2, 023116 (2023).

[4] Jun Zhang, Li-Hua Zhang, Bang Liu, Zheng-Yuan Zhang, Shi-Yao Shao, Qing Li, Han-Chao Chen, Zong-Kai Liu, Yu Ma, Tian-Yu Han, Qi-Feng Wang, C. Stuart Adams, Bao-Sen Shi, and Dong-Sheng Ding, "Early Warning Signals of the Tipping Point in Strongly Interacting Rydberg Atoms", Physical Review Letters 133 24, 243601 (2024).

[5] Yi Zhang, "Photon amplification and cavity-polariton-like generation in metallic nanoshells localized in optical cavity", Optics Express 31 4, 5640 (2023).

[6] K. E. Ballantine and J. Ruostekoski, "Unidirectional absorption, storage, and emission of single photons in a collectively responding bilayer atomic array", Physical Review Research 4 3, 033200 (2022).

[7] Jan Kumlin, Ajit Srivastava, and Thomas Pohl, "Superradiance of Strongly Interacting Dipolar Excitons in Moiré Quantum Materials", Physical Review Letters 134 12, 126901 (2025).

[8] J. Talukdar and D. Blume, "Photon-induced dropletlike bound states in a one-dimensional qubit array", Physical Review A 108 2, 023702 (2023).

[9] Jan Kumlin, Christoph Braun, Christoph Tresp, Nina Stiesdal, Sebastian Hofferberth, and Asaf Paris-Mandoki, "Quantum optics with Rydberg superatoms", Journal of Physics Communications 7 5, 052001 (2023).

[10] Yakov Solomons, Inbar Shani, Ofer Firstenberg, Nir Davidson, and Ephraim Shahmoon, "Efficient coupling of light to an atomic tweezer array in a cavity", Physical Review Research 6 4, L042070 (2024).

[11] Shiwen Sun, Yi-Xin Wang, Xiao Liu, and Yan Zhang, "Tunable dual-band atomic mirror based on subwavelength atomic arrays under electromagnetically induced transparency", Physical Review A 113 6, 063705 (2026).

[12] Roni Ben-Maimon, Yakov Solomons, and Ephraim Shahmoon, "Dissipative transfer of quantum correlations from light to atomic arrays", Physical Review A 110 3, 033719 (2024).

[13] Maxim Makhonin, Anthonin Delphan, Kok Wee Song, Paul Walker, Tommi Isoniemi, Peter Claronino, Konstantinos Orfanakis, Sai Kiran Rajendran, Hamid Ohadi, Julian Heckötter, Marc Assmann, Manfred Bayer, Alexander Tartakovskii, Maurice Skolnick, Oleksandr Kyriienko, and Dmitry Krizhanovskii, "Nonlinear Rydberg exciton-polaritons in Cu2O microcavities", Light: Science & Applications 13 1, 47 (2024).

[14] Yidan Wang, Oriol Rubies-Bigorda, Valentin Walther, and Susanne F. Yelin, "Multiexcitation scattering in subwavelength atomic arrays", Physical Review A 114 1, 013705 (2026).

[15] Danil Kornovan, Alexander Poddubny, and Alexander Poshakinskiy, "Long persistent anticorrelations in few-qubit arrays", Physical Review A 108 3, 033707 (2023).

[16] Ignacio R. Sola, Seokmin Shin, and Bo Y. Chang, "Two-qubit quantum gates with minimal pulse sequences", Physical Review A 109 5, 052603 (2024).

[17] Yakov Solomons, Roni Ben-Maimon, Arpit Behera, Ofer Firstenberg, Nir Davidson, and Ephraim Shahmoon, "Free-Space Quantum Interface of a Single Atomic Tweezer Array with Light", PRX Quantum 7 1, 010342 (2026).

[18] Yakov Solomons and Ephraim Shahmoon, "Multichannel waveguide QED with atomic arrays in free space", Physical Review A 107 3, 033709 (2023).

[19] Simon Panyella Pedersen, Georg M. Bruun, and Thomas Pohl, "Green's function approach to interacting lattice polaritons and optical nonlinearities in subwavelength arrays of quantum emitters", Physical Review Research 6 4, 043264 (2024).

[20] Lida Zhang, Fan Yang, Klaus Mølmer, and Thomas Pohl, "Unidirectional quantum-optical elements for waveguide-QED with subwavelength Rydberg-atom arrays in free space", Optica Quantum 3 3, 256 (2025).

[21] David Petrosyan, József Fortágh, and Gershon Kurizki, "Coherent interface between optical and microwave photons on an integrated superconducting atom chip", EPJ Quantum Technology 11 1, 18 (2024).

[22] Nicola Piovella and Romain Bachelard, "Subradiant Decay in 2D and 3D Atomic Arrays", Photonics 12 12, 1214 (2025).

[23] Kyle E. Ballantine and Janne Ruostekoski, "Cooperative optical wavefront engineering with atomic arrays", Nanophotonics 10 7, 1901 (2021).

[24] Alexandra S. Sheremet, Mihail I. Petrov, Ivan V. Iorsh, Alexander V. Poshakinskiy, and Alexander N. Poddubny, "Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations", Reviews of Modern Physics 95 1, 015002 (2023).

[25] C. D. Parmee, K. E. Ballantine, and J. Ruostekoski, "Spontaneous symmetry breaking in frustrated triangular atom arrays due to cooperative light scattering", Physical Review Research 4 4, 043039 (2022).

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[44] Li-Ping Yang and Dazhi Xu, "Quantum theory of photonic vortices and quantum statistics of twisted photons", Physical Review A 105 2, 023723 (2022).

[45] Ole A. Iversen and Thomas Pohl, "Self-ordering of individual photons in waveguide QED and Rydberg-atom arrays", Physical Review Research 4 2, 023002 (2022).

[46] Christopher Fechisin, Kunal Sharma, Przemyslaw Bienias, Steven L. Rolston, J. V. Porto, Michael J. Gullans, and Alexey V. Gorshkov, "Quantum Non-Demolition Photon Counting in a 2d Rydberg Atom Array", arXiv:2210.10798, (2022).

[47] Yakov Solomons and Ephraim Shahmoon, "Multi-channel waveguide QED with atomic arrays in free space", arXiv:2111.11515, (2021).

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