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We demonstrate hybridization of optical cavity photons with atomic Rydberg excitations using electromagnetically induced transparency (EIT). The resulting dark state Rydberg polaritons exhibit a compressed frequency spectrum and enhanced lifetime indicating strong light-matter mixing. We study the coherence properties of cavity Rydberg polaritons and identify the generalized EIT linewidth for optical cavities. Strong collective coupling suppresses polariton losses due to inhomogeneous broadening, which we demonstrate by using different Rydberg levels with a range of polarizabilities. Our results point the way towards using cavity Rydberg polaritons as a platform for creating photonic quantum materials.PACS numbers: 42.50. Gy, 42.50.Pq, 32.80.Ee, 71.36.+c Coupling photons to electronic excitations of a medium leads to hybrid quasiparticles, or polaritons, that carry properties of both light and matter. The photonic component allows polaritons to propagate like light, while the material component enables interactions between polaritons. An important example is exciton polaritons in semiconductor microcavities, which exhibit an effective mass and two-dimensional motion arising from the photonic component, while the exciton component leads to a mean-field interaction, allowing Bose-Einstein condensation [1][2][3]. Rydberg polaritons in atomic gases enable strong interactions even at the few-quantum level [4][5][6][7][8][9][10][11][12], a key ingredient for producing highly correlated states, including fractional quantum Hall states [13][14][15][16][17] and emergent quantum crystals [17][18][19][20][21]. While previous work on Rydberg polaritons has focused on onedimensional free-space light fields, photons in optical cavities provide access to two-dimensional motion, harmonic trapping [22], and effective magnetic fields [17,23]. In addition, optical cavities can enhance the optical nonlinearity arising from Rydberg interactions [24,25].Rydberg polaritons are formed by coherently coupling light to a highly excited atomic Rydberg level using electromagnetically induced transparency (EIT) [26]. At EIT resonance, destructive interference prevents population of a lossy intermediate atomic level, resulting in a dark state polariton [27] that consists of a superposition of a photon and a collective atomic Rydberg excitation. A large admixture of the (long-lived) atomic excitation in a dark state polariton slows all photonic dynamics [27]. In an optical cavity, this results in a polariton whose lifetime can exceed the empty-cavity lifetime by orders of magnitude, and an energy that is pulled toward the EIT resonance [28][29][30][31][32][33]. In a multimode cavity, hybridization rescales the trap frequency and effective mass of the polariton [17].We experimentally observe Rydberg polaritons in an optical cavity and explore the spectral and coherence properties of these collective states in cavity transmission spectroscopy. While Doppler decoherence and inhomogeneous Stark shifts [35][36][37] are more significant for Rydbe...

Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions [1][2][3][4][5][6], raising the prospect of forming synthetic materials [7] and quantum information systems [8][9][10][11] from photons. One promising approach uses electromagnetically-induced transparency with highly-excited Rydberg atoms to generate strong photonic interactions [12][13][14][15][16][17][18][19]. Adding an optical cavity shapes the available modes and forms strongly-interacting polaritons with enhanced light-matter coupling [20][21][22]. However, since every atom of the same species is identical, the atomic transitions available are only those prescribed by nature. This inflexibility severely limits their utility for mediating the formation of photonic materials in cavities, as the resonator mode spectrum is typically poorly matched to the atomic spectrum. Here we use Floquet engineering [23,24] to redesign the spectrum of Rubidium and make it compatible with the spectrum of a cavity, in order to explore strongly interacting polaritons in a customized space. We show that periodically modulating the energy of an atomic level redistributes its spectral weight into lifetime-limited bands separated by multiples of the modulation frequency. Simultaneously generating bands resonant with two chosen spatial modes of an optical cavity supports "Floquet polaritons" in both modes. In the presence of Rydberg dressing, we find that these polaritons interact strongly. Floquet polaritons thus provide a promising new path to quantum information technologies such as multimode photonby-photon switching, as well as to ordered states of strongly-correlated photons, including crystals and topological fluids. arXiv:1806.10621v1 [cond-mat.quant-gas]

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