Cavity Mediated Rydberg Quantum Phase Transitions

This chapter focuses on collective many-body phenomena arising in cavity-coupled Rydberg ensembles. The superradiant phase transition of cavity-Rydberg polaritons is discussed, along with the enhancement of superradiance by strong RydbergRydberg interactions. The analysis extends to ordered phases in two-dimensional Rydberg arrays and phase transitions in cold-atom lattices. Particular emphasis is placed on the interplay of local versus nonlocal quantum dynamics, string dynamics, and emergent correlations, which highlight the rich nonequilibrium physics accessible in these systems.