Quantum Phase Transitions in Many-Dipole Light-Matter Systems

A potential phase transition between a normal ground state and a photon-condensed ground state in many-dipole light-matter systems is a topic of considerable controversy, exasperated by conflicting no-go and counter no-go theorems and often ill-defined models. We clarify this long-lasting debate by analyzing two specific arrangements of atoms, including a 3D cubic lattice and a cavity-embedded square lattice layer, which provides a physical model for single-mode cavity QED with coupled dipoles in the thermodynamic limit. These models are shown to significantly differ from the standard Dicke model and, in the thermodynamic limit, give rise to renormalized Hopfield models. We show that a ferroelectric phase transition can (in principle) still occur and the description of the abnormal phase beyond the critical point requires the inclusion of nonlinear terms in the Holstein-Primakoff mapping. We also show how our model agrees with recent experiments.