Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties [1][2][3][4][5]. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science [6][7][8]. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip [9]. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock-Darwin Hamiltonian for photons in a magnetic field and harmonic trap [10]. Using spatialand energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit [10,11], we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen-Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space [12][13][14][15]. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids [16,17] and direct detection of anyons [18,19].The Lorentz force on a charged particle moving in a magnetic field leads to the unique topological features of quantum Hall systems, including precisely quantized Hall conductance, topologically protected edge transport, and, in the presence of interactions, the predicted anyonic and non-abelian braiding statistics that form the basis of topological quantum computing [20]. To controllably explore the emergence of these phenomena, efforts have recently focused on realizing synthetic materials in artificial magnetic fields, and in particular, upon implementations for cold atoms and photons. Successful photonic implementations have employed lattices with engineered tunneling [6,[21][22][23][24]. However, it is desirable to realize artificial magnetic fields in the simpler case of a continuum (lattice-free) material [7,25,26], where strong interactions are more easily accessible and the theory maps more directly to fractional quantum Hall systems. In this work, we develop a new approach and demonstrate the first continuum synthetic magnetic field for light.To achieve photonic Landau levels we harness the powerful analogy between photons in a near-degenerate multimode cavity and massive, trapped 2d particles [27,28]. Owing to mirror curvature, the transverse dynamics of a running wave resonator are equivalent to those of a 2D quantum h...
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...
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