Bose condensation in a model microcavity

We study the equilibrium properties of a system of dipole-active excitons coupled to a single photon mode at fixed total excitation. Treating the presence or absence of a trapped exciton as a two-level system produces a model, the Dicke model, that is exactly soluble. It gives a simple description of polariton condensation in optical cavities, beyond the low-density bosonic regime.