Nucleation of superfluid-light domains

Electromagnetic coupled resonator arrays (CRAs) doped with a quantum two-level system allow for the quantum simulation of a Mott-insulator to superfluid phase transition. We demonstrate that the order of this simulated phase transition depends on the type of dynamics. Thus, a first order like phase transition can be induced by a quench dynamics, while a second order like phase transition is produced by an adiabatic dynamics. In addition, we show that the underlying macroscopic behavior of the phase transition in other many body systems, such as domain nucleation and phase coexistence, can also be observed in CRAs. This universal behavior emerges from the light-matter interaction and the topology of the array. Therefore, the latter can be used to manipulate the photonic transport properties of the simulated super fluid phase.