Floquet Route to Non-Equilibrium Phases of Matter in Cavity QED

Time-periodic (Floquet) drive has become a powerful tool to engineer new phases of matter, both in equilibrium and far from equilibrium. In this talk, I show that this structure maps to unexpected phases of coupled light in matter in similar systems where the drive photons are treated as quantized degrees of freedom, namely many-body cavity quantum electrodynamics (QED). This is non-trivial even for such “basic” phenomena as many body localization, where the localizing interactions compete against global coupling to the quantized cavity mode. I will survey ways in which this competition gives rise to unusual phenomena such as an inverted mobility edge, with delocalization at low energies, and localization induced by coupling to the global cavity mode. I will also show that interesting topological structures can emerge with quantized pumping of the cavity mode(s). These ideas may have experimental relevance from conventional many body cavity QED systems using ultracold atoms to more recent cavity QED-like setups such as superconducting circuit QED and central spin models.