Programmable quantum simulations in an optical cavity: from collective spins towards single atoms

Interactions within a quantum system dictate the structure of entanglement between its constituents. Control of this structure is necessary for analog quantum simulation and novel quantum sensing protocols. Most platforms for quantum science are limited to spatially local interactions, but the photon-mediated interactions inherent to cavity QED systems naturally generate distance agnostic all-to-all interactions, providing new capabilities for engineering interaction graphs with tailored nonlocal connectivity. Essential for harnessing these interactions is strong atom-cavity coupling, quantified by the single-atom cooperativity C. We present the development of an upgraded near-concentric optical cavity QED apparatus designed to achieve a cooperativity C~100, two orders of magnitude larger than the strong coupling criterion. We additionally present investigations in an existing apparatus, where we rely on collectively enhanced atom-light interactions in an array of atomic ensembles to engineer tailored graphs. We illustrate the unique capabilities of this toolbox for probing topological phases of matter and simulating aspects of holographic duality, and touch on prospects for extending cavity-enabled quantum simulations into a strongly interacting regime.