Degenerate Multimode Cavities for Topological Quantum Optics with Rydberg Polaritons

Realizing fractional Quantum Hall states in quantum simulation experiments is a long-standing goal on the way to understanding and harnessing topological states of matter. Initial progress has been demonstrated with our realization of a two-photon Laughlin state [1] and recently the demonstration of a two-atom Laughlin state in an optical lattice [2], stimulating the quest to prepare bigger systems where true many-body properties like anyonic quasi particles become accessible. Our hybrid platform uses cavity Rydberg polaritons, quasiparticles of an optical cavity photon hybridized with an interacting atomic Rydberg excitation, to create interactions and artificial gauge fields for light. We will present our new, aspheric lens based degenerate multimode cavity that will allow approaching mesoscopic system sizes, and first experimental results using this platform on the way to larger Quantum Hall states.

[1] Logan W Clark, Nathan Schine, Claire Baum, Ningyuan Jia and Jonathan Simon, "Observation of Laughlin states made of light" Nature 582, 41-45, (2020)

[2] Julian Léonard, Sooshin Kim, Joyce Kwan, Perrin Segura, Fabian Grusdt, et al. "Realization of a fractional quantum Hall state with ultracold atoms", arXiv:2210.10919v1