Exploring measurement and feedback with ultracold atoms in an optical cavity

By placing ultracold atoms within an optical cavity, we couple a many-body quantum system with a single mode of light.  This light serves a dual role, both as an actuator on and mediator of interactions among the atoms, and also as an information carrier that allows sensitive measurement, potentially in vivo, of the quantum system.  I will discuss experiments performed on optical cavities containing either large atomic ensembles or mesoscopic atomic systems constructed atom-by-atom using optical tweezer arrays.  We demonstrate how the response of an optical cavity to the collective spin of an ensemble can effect autonomous feedback stabilization to a non-equilibrium steady state.  Sensitivity to single atomic spins enables mid-circuit measurement on an atom tweezer array, a prelude to implementing feedback and error correction.  Lastly, we explore the collective optical response of a structured array of atoms, demonstrating super- and sub-radiant Rayleigh scattering.  This collective optical response sets the stage for future experiments on light-mediated forces and a quantum-gas-microscope approach to studying phase transitions in open quantum systems.