Engineering strong non-local interactions in a near-concentric cavity

Photon-mediated interactions among atoms coupled to an optical cavity are a powerful tool for engineering quantum many-body Hamiltonians. We present an experiment aimed at generating non-local and dynamically controllable spin-spin interactions by strongly coupling 87Rb atoms to a near-concentric cavity. The tightly-focused waist of 11um combined with a high finesse of 60,000 yields a single-atom cooperativity of 50. Furthermore, the optical access afforded by the near-concentric geometry enables imaging and addressing with 1um resolution. We detail the current status of the experiment and progress toward many-body quantum control.