Engineering Programmable Interactions with an Optical Cavity

Tuneable, long-range interactions facilitate the study of quantum phenomena including integrability and fast scrambling. In our system, a driven optical cavity naturally mediates all-to-all interactions along a 1D chain of atomic ensembles. We break the global symmetry of these interactions by adding a gradient that dephases interactions between spatially separated ensembles. Interactions at specified distances are selectively re-introduced by modulating the drive field. Local addressing and in-situ imaging facilitate detailed exploration of dynamics on effective geometries specified by the graph of couplings. Realized geometries include 2D surfaces and a Moebius ladder, and we find that the dynamics are well described by the engineered dispersion relation. Current directions include probing entanglement and frustrastration in varied interaction graphs with applications in precision measurement and quantum simulation.