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Interacting Floquet polaritons


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.


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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.

Author information

Authors and Affiliations



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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The authors declare no competing interests.

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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).

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