Theory of photon condensation in a spatially varying electromagnetic field
Whether or not superradiant phase transitions (photon condensates) can occur in equilibrium systems is a long-debated open question. The realization of photon condensation in a spatially uniform cavity field is forbidden by a ``no-go'' theorem stemming from gauge invariance. Here, bypassing the theorem by considering a spatially varying electromagnetic field, the authors derive a series of criteria for the occurrence of photon condensation. The cases of both three-dimensional and two-dimensional electronic systems are analyzed. This work paves the way for the realization of equilibrium photon condensation in solid-state systems.