Recurrent delocalization and quasiequilibration of photons in coupled systems in circuit quantum electrodynamics

We explore the photon population dynamics in two coupled circuit QED systems. For a sufficiently weak intercavity photon hopping, as the photon-cavity coupling increases, the dynamics undergoes double transitions first from a delocalized to a localized phase and then from the localized to another delocalized phase. The latter delocalized phase is distinguished from the former one; instead of oscillating between the two cavities, the photons rapidly quasiequilibrate over the two cavities. These intriguing features are attributed to an interplay between two qualitatively distinctive nonlinear behaviors of the circuit QED systems in the utrastrong coupling regime, whose distinction has been widely overlooked.