- Physical Review Journals
All JournalsPhysics Magazine

PRX Quantum

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Multiband Dispersion and Warped Vortices of Strongly Interacting Photons

Bankim Chandra Das*, Dmytro Kiselov, Lee Drori, Ariel Nakav, Alexander Poddubny, and Ofer Firstenberg

  • *Contact author: bankim.das@weizmann.ac.il
PDF

PRX Quantum 7, 043002 – Published 2 October, 2026

DOI: https://doi.org/10.1103/mndb-nzqd

Abstract

We present a theoretical study of quantum correlations between interacting photons realized through co-propagating Rydberg polaritons. We show that the spatial evolution of the n-photon wavefunction is governed by a multiband dispersion featuring one massive mode and multiple massless modes with degenerate Dirac points and n-fold rotational symmetry. The resulting band structure is warped, departing from the single-band, parabolic approximation commonly assumed for interacting polaritons. Our analytical results are supported by rigorous numerical modeling that fully accounts for photon propagation inside the finite atomic medium. These findings advance the understanding of multiphoton interactions and support the development of future multiphoton control tools.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

We predict a new class of quantum few-body effects arising from the multicomponent nature of the strongly interacting photons realized in a gas of cold Rydberg atoms. We show that the internal degrees of freedom inherited from the coupled light and matter fundamentally modify the multicomponent states, resulting in interaction-induced symmetry reduction and warped vortex structures of photons. These results are absent in the well-established single-component approximations and are confirmed by both numerical and analytical methods we developed. Our findings connect quantum nonlinear optics with concepts from multiband and topological quantum matter. The predicted effects are experimentally accessible through photon correlation measurements. The reduced symmetry has direct implications for the topology and propagation dynamics of the polariton wavefunction, including the possibility of vortex formation outside of the interaction medium seeded during the interaction.

Article Text

References (37)

  1. C. Murray and T. Pohl, Quantum and nonlinear optics in strongly interacting atomic ensembles, in Advances in Atomic, Molecular, and Optical Physics (Academic Press, Cambridge, MA, USA, 2016), Vol. 65, pp. 321–372.
  2. O. Firstenberg, C. S. Adams, and S. Hofferberth, Nonlinear quantum optics mediated by Rydberg interactions, J. Phys. B 49, 152003 (2016).
  3. D. E. Chang, V. Vuletić, and M. D. Lukin, Quantum nonlinear optics—photon by photon, Nat. Photonics 8, 685 (2014).
  4. T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletić, Quantum nonlinear optics with single photons enabled by strongly interacting atoms, Nature (London) 488, 57 (2012).
  5. H. Gorniaczyk, C. Tresp, J. Schmidt, H. Fedder, and S. Hofferberth, Single-photon transistor mediated by interstate Rydberg interactions, Phys. Rev. Lett. 113, 053601 (2014).
  6. S. Baur, D. Tiarks, G. Rempe, and S. Dürr, Single-photon switch based on Rydberg blockade, Phys. Rev. Lett. 112, 073901 (2014).
  7. D. P. Ornelas-Huerta, P. Bienias, A. N. Craddock, M. J. Gullans, A. J. Hachtel, M. Kalinowski, M. E. Lyon, A. V. Gorshkov, S. L. Rolston, and J. V. Porto, Tunable three-body loss in a nonlinear Rydberg medium, Phys. Rev. Lett. 126, 173401 (2021).
  8. D. Tiarks, S. Schmidt, G. Rempe, and S. Dürr, Optical π phase shift created with a single-photon pulse, Sci. Adv. 2, e1600036 (2016).
  9. 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, Symmetry-protected collisions between strongly interacting photons, Nature (London) 542, 206 (2017).
  10. O. Firstenberg, T. Peyronel, Q.-Y. Liang, A. V. Gorshkov, M. D. Lukin, and V. Vuletić, Attractive photons in a quantum nonlinear medium, Nature (London) 502, 71 (2013).
  11. N. Stiesdal, J. Kumlin, K. Kleinbeck, P. Lunt, C. Braun, A. Paris-Mandoki, C. Tresp, H. P. Büchler, and S. Hofferberth, Observation of three-body correlations for photons coupled to a Rydberg superatom, Phys. Rev. Lett. 121, 103601 (2018).
  12. Q.-Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin, and V. Vuletić, Observation of three-photon bound states in a quantum nonlinear medium, Science 359, 783 (2018).
  13. H. Busche, P. Huillery, S. W. Ball, T. Ilieva, M. P. A. Jones, and C. S. Adams, Contactless nonlinear optics mediated by long-range Rydberg interactions, Nat. Phys. 13, 655 (2017).
  14. L. W. Clark, N. Jia, N. Schine, C. Baum, A. Georgakopoulos, and J. Simon, Interacting Floquet polaritons, Nature (London) 571, 532 (2019).
  15. L. Drori, B. C. Das, T. D. Zohar, G. Winer, E. Poem, A. Poddubny, and O. Firstenberg, Quantum vortices of strongly interacting photons, Science 381, 193 (2023).
  16. K. Jachymski, P. Bienias, and H. P. Büchler, Three-body interaction of Rydberg slow-light polaritons, Phys. Rev. Lett. 117, 053601 (2016).
  17. M. J. Gullans, J. D. Thompson, Y. Wang, Q.-Y. Liang, V. Vuletić, M. D. Lukin, and A. V. Gorshkov, Effective field theory for Rydberg polaritons, Phys. Rev. Lett. 117, 113601 (2016).
  18. A. Grankin, P. Grangier, and E. Brion, Diagrammatic treatment of few-photon scattering from a Rydberg-blockaded atomic ensemble in a cavity, Phys. Rev. A 98, 053860 (2018).
  19. M. Kalinowski, Y. Wang, P. Bienias, M. J. Gullans, D. P. Ornelas-Huerta, A. N. Craddock, S. L. Rolston, J. V. Porto, H. P. Büchler, and A. V. Gorshkov, Resonant enhancement of three-body loss between strongly interacting photons, Phys. Rev. Res. 4, L022059 (2022).
  20. T. Caneva, M. T. Manzoni, T. Shi, J. S. Douglas, J. I. Cirac, and D. E. Chang, Quantum dynamics of propagating photons with strong interactions: A generalized input–output formalism, New J. Phys. 17, 113001 (2015).
  21. Z. Chen, Y. Zhou, and J.-T. Shen, Correlation signatures for a coherent three-photon scattering in waveguide quantum electrodynamics, Opt. Lett. 45, 2559 (2020).
  22. A. S. Sheremet, M. I. Petrov, I. V. Iorsh, A. V. Poshakinskiy, and A. N. Poddubny, Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations, Rev. Mod. Phys. 95, 015002 (2023).
  23. G. Calajó and D. E. Chang, Emergence of solitons from many-body photon bound states in quantum nonlinear media, Phys. Rev. Res. 4, 023026 (2022).
  24. A. Denisov, H. M. Castro-Beltran, and H. J. Carmichael, Time-asymmetric fluctuations of light and the breakdown of detailed balance, Phys. Rev. Lett. 88, 243601 (2002).
  25. M. Koch, C. Sames, M. Balbach, H. Chibani, A. Kubanek, K. Murr, T. Wilk, and G. Rempe, Three-photon correlations in a strongly driven atom-cavity system, Phys. Rev. Lett. 107, 023601 (2011).
  26. A. V. Gorshkov, J. Otterbach, M. Fleischhauer, T. Pohl, and M. D. Lukin, Photon-photon interactions via Rydberg blockade, Phys. Rev. Lett. 107, 133602 (2011).
  27. B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
  28. S. Taneda and H. Honji, Unsteady flow past a flat plate normal to the direction of motion, J. Phys. Soc. Jpn. 30, 262 (1971).
  29. G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, Single vortex–antivortex pair in an exciton-polariton condensate, Nat. Phys. 7, 129 (2011).
  30. L. Levitov and G. Falkovich, Electron viscosity, current vortices and negative nonlocal resistance in graphene, Nat. Phys. 12, 672 (2016).
  31. P. Bienias, S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D. Lukin, A. V. Gorshkov, and H. P. Büchler, Scattering resonances and bound states for strongly interacting Rydberg polaritons, Phys. Rev. A 90, 053804 (2014).
  32. J. P. Leroy and R. Wallace, Procedures leading to a variety of orthonormal Jacobi-type coordinates of relevance to large-amplitude vibration and scattering problems, Chem. Phys. 111, 11 (1987).
  33. M. Orlita, D. M. Basko, M. S. Zholudev, F. Teppe, W. Knap, V. I. Gavrilenko, N. N. Mikhailov, S. A. Dvoretskii, P. Neugebauer, C. Faugeras, A.-L. Barra, G. Martinez, and M. Potemski, Observation of three-dimensional massless Kane fermions in a zinc-blende crystal, Nat. Phys. 10, 233 (2014).
  34. Z. Rao, H. Li, T. Zhang, S. Tian, C. Li, B. Fu, C. Tang, L. Wang, Z. Li, W. Fan, J. Li, Y. Huang, Z. Liu, Y. Long, C. Fang, H. Weng, Y. Shi, H. Lei, Y. Sun, T. Qian, and H. Ding, Observation of unconventional chiral fermions with long Fermi arcs in CoSi, Nature (London) 567, 496 (2019).
  35. G. E. Volovik, The Universe in a Helium Droplet (Oxford University, Oxford, 2003), Vol. 117.
  36. K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, Observation of half-quantum vortices in an exciton-polariton condensate, Science 326, 974 (2009).
  37. J. Kumlin, C. Braun, C. Tresp, N. Stiesdal, S. Hofferberth, and A. Paris-Mandoki, Quantum optics with Rydberg superatoms, J. Phys. Commun. 7, 052001 (2023).

Outline

Information

PRX Quantum 7, 043002– Published 2 October, 2026
  • Received 16 May 2026
  • Accepted 10 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation