Quantum Manybody Physics in Multimode Cavities & Cavity Arrays

In this talk I would describe the current state-of-the-art in the Simon/Schuster collaboration at Stanford, where we explore novel cavity architectures fort manybody physics. I'll begin with a description of our newly upgraded twisted resonator topological fluid experiments, where optical photons residing in the lowest landau level of a multimode cavity interact through Rydberg dressing to explore mean-field and fractional-quantum-hall physics. From here I'll speak briefly about our recent demonstrations of strongly interacting fluids and solids of microwave photons in transmon arrays, culminating in a new ancilla-controlled interferometry technique that suggests new opportunities to leverage quantum computers to probe quantum matter. Finally, I will conclude with a brief introduction to our new optical-cavity-array platform, that we have recently integrated with an atom-array, with prospects in quantum computing and networking, but also exotic Jaynes-Cummings-Hubbard models of strongly interacting optical photons.