Degenerate Multimode Cavities for Topological Quantum Optics with Rydberg Polaritons

Quantum simulation experiments provide a unique opportunity to realize, manipulate, and understand fractional Quantum Hall states with a high degree of controllability.

Initial progress towards this long-standing goal has been demonstrated with our realization of a two-photon Laughlin state [1] and of a two-atom Laughlin state in an optical lattice [2], stimulating the quest to prepare bigger systems where true many-body properties, like exotic anyonic excitations, are accessible.

Our experimental platform hybridizes photons in a twisted optical cavity with atomic Rydberg excitations to create a system of itinerant, strongly interacting particles in an artificial gauge field.

We will present first results using our aspheric lens-based degenerate twisted multimode cavity realizing a lowest Landau level for a mesoscopic number of photons. With increasing Rydberg interaction strength, we can access a series of interesting states from the mean field regime towards strongly correlated states such as the Laughlin state. Combined with new imaging capabilities, we show the first data of spatially-resolved interacting polaritons 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] Léonard, J., Kim, S., Kwan, J. et al. Realization of a fractional quantum Hall state with ultracold atoms. Nature 619, 495–499 (2023)