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Interacting Floquet polaritons

Abstract

Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions1,2, raising the prospect of forming synthetic materials3 and quantum information systems4,5,6,7 from photons. One promising approach combines highly excited Rydberg atoms8,9,10,11,12 with the enhanced light–matter coupling of an optical cavity to convert photons into strongly interacting polaritons13,14,15. However, quantum materials made of optical photons have not yet been realized, because the experimental challenge of coupling a suitable atomic sample with a degenerate cavity has constrained cavity polaritons to a single spatial mode that is resonant with an atomic transition. Here we use Floquet engineering16,17—the periodic modulation of a quantum system—to enable strongly interacting polaritons to access multiple spatial modes of an optical cavity. First, we show that periodically modulating an excited state of rubidium splits its spectral weight to generate new lines—beyond those that are ordinarily characteristic of the atom—separated by multiples of the modulation frequency. Second, we use this capability to simultaneously generate spectral lines that are resonant with two chosen spatial modes of a non-degenerate optical cavity, enabling what we name ‘Floquet polaritons’ to exist in both modes. Because both spectral lines correspond to the same Floquet-engineered atomic state, adding a single-frequency field is sufficient to couple both modes to a Rydberg excitation. We demonstrate that the resulting polaritons interact strongly in both cavity modes simultaneously. The production of Floquet polaritons provides a promising new route to the realization of ordered states of strongly correlated photons, including crystals and topological fluids, as well as quantum information technologies such as multimode photon-by-photon switching.

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Fig. 1: Redistributing the spectral density of atoms coupled to a cavity.
Fig. 2: Forming Floquet polaritons in a customized space.
Fig. 3: Strong interactions between Floquet dark polaritons.

Data availability

The experimental data presented in this manuscript is available from the corresponding author upon request.

References

  1. Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).

    ADS  CAS  PubMed  Google Scholar 

  2. Chang, D. E., Vuletić, V. & Lukin, M. D. Quantum nonlinear optics—photon by photon. Nat. Photon. 8, 685–694 (2014).

    ADS  CAS  Google Scholar 

  3. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    ADS  Google Scholar 

  4. Raimond, J. M., Brune, M. & Haroche, S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001).

    ADS  MathSciNet  MATH  Google Scholar 

  5. Duan, L.-M., Lukin, M., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001).

    ADS  CAS  PubMed  Google Scholar 

  6. Kimble, H. J. The quantum internet. Nature 453, 1023–1030 (2008).

    ADS  CAS  PubMed  Google Scholar 

  7. Saffman, M., Walker, T. G. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    ADS  CAS  Google Scholar 

  8. Peyronel, T. et al. Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57–60 (2012).

    ADS  CAS  PubMed  Google Scholar 

  9. Dudin, Y., Li, L., Bariani, F. & Kuzmich, A. Observation of coherent many-body Rabi oscillations. Nat. Phys. 8, 790–794 (2012).

    CAS  Google Scholar 

  10. Tiarks, D., Baur, S., Schneider, K., Dürr, S. & Rempe, G. Single-photon transistor using a Förster resonance. Phys. Rev. Lett. 113, 053602 (2014).

    ADS  PubMed  Google Scholar 

  11. Gorniaczyk, H., Tresp, C., Schmidt, J., Fedder, H. & Hofferberth, S. Single-photon transistor mediated by interstate Rydberg interactions. Phys. Rev. Lett. 113, 053601 (2014).

    ADS  CAS  PubMed  Google Scholar 

  12. Thompson, J. D. et al. Symmetry-protected collisions between strongly interacting photons. Nature 542, 206–209 (2017).

    ADS  CAS  PubMed  Google Scholar 

  13. Guerlin, C., Brion, E., Esslinger, T. & Mølmer, K. Cavity quantum electrodynamics with a Rydberg-blocked atomic ensemble. Phys. Rev. A 82, 053832 (2010).

    ADS  Google Scholar 

  14. Jia, N. et al. A strongly interacting polaritonic quantum dot. Nat. Phys. 14, 550–554 (2018).

    CAS  Google Scholar 

  15. Georgakopoulos, A., Sommer, A. & Simon, J. Theory of interacting cavity Rydberg polaritons. Quantum Sci. Technol. 4, 014005 (2018).

    ADS  Google Scholar 

  16. Silveri, M. P., Tuorila, J. A., Thuneberg, E. V. & Paraoanu, G. S. Quantum systems under frequency modulation. Rep. Prog. Phys. 80, 056002 (2017).

    ADS  CAS  PubMed  Google Scholar 

  17. Eckardt, A. Atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017).

    ADS  MathSciNet  Google Scholar 

  18. Fleischhauer, M., Imamoglu, A. & Marangos, J. Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005).

    ADS  CAS  Google Scholar 

  19. Douglas, J. S. et al. Quantum many-body models with cold atoms coupled to photonic crystals. Nat. Photon. 9, 326–331 (2015).

    ADS  CAS  Google Scholar 

  20. Schine, N., Ryou, A., Gromov, A., Sommer, A. & Simon, J. Synthetic Landau levels for photons. Nature 534, 671–675 (2016).

    ADS  CAS  PubMed  Google Scholar 

  21. Lim, H.-T., Togan, E., Kroner, M., Miguel-Sanchez, J. & Imamoğlu, A. Electrically tunable artificial gauge potential for polaritons. Nat. Commun. 8, 14540 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  22. Schine, N., Chalupnik, M., Can, T., Gromov, A. & Simon, J. Electromagnetic and gravitational responses of photonic Landau levels. Nature 565, 173–179 (2019).

    ADS  CAS  PubMed  Google Scholar 

  23. Strand, J. D. et al. First-order sideband transitions with flux-driven asymmetric transmon qubits. Phys. Rev. B 87, 220505 (2013).

    ADS  Google Scholar 

  24. Naik, R. et al. Random access quantum information processors using multimode circuit quantum electrodynamics. Nat. Commun. 8, 1904 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  25. Beaudoin, F., da Silva, M. P., Dutton, Z. & Blais, A. First-order sidebands in circuit QED using qubit frequency modulation. Phys. Rev. A 86, 022305 (2012).

    ADS  Google Scholar 

  26. Beaufils, Q. et al. Radio-frequency association of molecules: an assisted Feshbach resonance. Eur. Phys. J. D 56, 99–104 (2010).

    ADS  CAS  Google Scholar 

  27. Ningyuan, J. et al. Observation and characterization of cavity Rydberg polaritons. Phys. Rev. A 93, 041802 (2016).

    ADS  Google Scholar 

  28. Zeuthen, E., Gullans, M. J., Maghrebi, M. F. & Gorshkov, A. V. Correlated photon dynamics in dissipative Rydberg media. Phys. Rev. Lett. 119, 043602 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  29. Ivanov, P. A., Letscher, F., Simon, J. & Fleischhauer, M. Adiabatic flux insertion and growing of Laughlin states of cavity Rydberg polaritons. Phys. Rev. A 98, 013847 (2018).

    ADS  CAS  Google Scholar 

  30. Dutta, S. & Mueller, E. Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles. Phys. Rev. A 97, 033825 (2018).

    ADS  CAS  Google Scholar 

  31. Sommer, A., Büchler, H. P. & Simon, J. Quantum crystals and Laughlin droplets of cavity Rydberg polaritons. Preprint at https://arxiv.org/abs/1506.00341 (2015).

  32. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    ADS  MathSciNet  CAS  Google Scholar 

  33. Norcia, M. A., Cline, J. R. K., Bartolotta, J. P., Holland, M. J. & Thompson, J. K. Narrow-line laser cooling by adiabatic transfer. New J. Phys. 20, 023021 (2018).

    ADS  Google Scholar 

  34. Ma, R. et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett. 107, 095301 (2011).

    ADS  PubMed  Google Scholar 

  35. Parker, C. V., Ha, L.-C. & Chin, C. Direct observation of effective ferromagnetic domains of cold atoms in a shaken optical lattice. Nat. Phys. 9, 769–774 (2013).

    CAS  Google Scholar 

  36. Clark, L. W., Feng, L. & Chin, C. Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition. Science 354, 606–610 (2016).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  37. Daley, A. J. & Simon, J. Effective three-body interactions via photon-assisted tunneling in an optical lattice. Phys. Rev. A 89, 053619 (2014).

    ADS  Google Scholar 

  38. Meinert, F., Mark, M. J., Lauber, K., Daley, A. J. & Nägerl, H.-C. Floquet engineering of correlated tunneling in the Bose–Hubbard model with ultracold atoms. Phys. Rev. Lett. 116, 205301 (2016).

    ADS  CAS  PubMed  Google Scholar 

  39. Clark, L. W., Gaj, A., Feng, L. & Chin, C. Collective emission of matter-wave jets from driven Bose–Einstein condensates. Nature 551, 356–359 (2017).

    ADS  CAS  PubMed  Google Scholar 

  40. Lignier, H. et al. Dynamical control of matter-wave tunneling in periodic potentials. Phys. Rev. Lett. 99, 220403 (2007).

    ADS  CAS  PubMed  Google Scholar 

  41. Struck, J. et al. Tunable gauge potential for neutral and spinless particles in driven optical lattices. Phys. Rev. Lett. 108, 225304 (2012).

    ADS  CAS  PubMed  Google Scholar 

  42. Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).

    ADS  CAS  PubMed  Google Scholar 

  43. Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013).

    ADS  PubMed  Google Scholar 

  44. Tai, M. E. et al. Microscopy of the interacting Harper–Hofstadter model in the two-body limit. Nature 546, 519–523 (2017).

    ADS  CAS  PubMed  Google Scholar 

  45. Clark, L. W. et al. Observation of density-dependent gauge fields in a Bose–Einstein condensate based on micromotion control in a shaken two-dimensional lattice. Phys. Rev. Lett. 121, 030402 (2018).

    ADS  CAS  PubMed  Google Scholar 

  46. Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).

    ADS  CAS  PubMed  Google Scholar 

  47. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2015).

    CAS  Google Scholar 

  48. Tarnowski, M. et al. Measuring topology from dynamics by obtaining the Chern number from a linking number. Nat. Commun. 10, 1728 (2019).

    ADS  Google Scholar 

  49. Fläschner, N. et al. Observation of dynamical vortices after quenches in a system with topology. Nat. Phys. 14, 265–268 (2018).

    Google Scholar 

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Acknowledgements

We thank L. Feng for comments on the manuscript. This work was supported by DOE grant DE-SC0010267 for apparatus construction, AFOSR grant FA9550-18-1-0317 for modelling and MURI grant FA9550-16-1-0323 for data collection and analysis. N.S. acknowledges support from a University of Chicago Grainger graduate fellowship and C.B. acknowledges support from the NSF GRFP.

Reviewer information

Nature thanks Oliver Morsch, Michael Sentef and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations

Authors

Contributions

The experiment was designed and built by all authors. L.W.C., N.J. and N.S. collected the data. L.W.C. and N.J. analysed the data. L.W.C. and J.S. developed the theory. L.W.C. prepared the manuscript, and all authors contributed to the final manuscript.

Corresponding author

Correspondence to Logan W. Clark.

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Extended data figures and tables

Extended Data Fig. 1 Atomic level diagram.

a, Three key electronic transitions of 87Rb atoms enable the formation of Floquet polaritons. First, cavity photons near 780 nm couple to the 5S1/2 → 5P3/2 atomic transition. Second, a beam near 480 nm drives the 5P3/2 → nS1/2 transition to the Rydberg level with principal quantum number n at coupling strength Ω. Third, a multichromatic field near the 5P3/2 → 5D5/2 transition modulates the energy of the 5P3/2 state. b, The multichromatic field has two components with approximately opposite detunings ±δ: a red-detuned component with constant intensity Ir, and a blue-detuned component with sinusoidally modulated intensity Ib[1 + cos(ωt)], where ω = 2πf.

Supplementary information

Supplementary Information

The supplementary information document provides experimental and theoretical details for this work. It contains three experimental sections discussing the analysis of the band strengths, correlations, and making comparisons to other possible modulation schemes. It contains nine theoretical sections discussing our model for the atom-cavity system, the nature of collective atomic excitations, and redistribution of a state using frequency modulation, Floquet polaritons in the high frequency approximation, the quasienergy spectrum, applications for Floquet polaritons, the connection to shaken optical lattices, the cause of asymmetric band strengths, and the multimode non-Hermitian perturbation theory.

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Clark, L.W., Jia, N., Schine, N. et al. Interacting Floquet polaritons. Nature 571, 532–536 (2019). https://doi.org/10.1038/s41586-019-1354-5

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