We study the equilibrium properties of a system of dipole-active excitons c
oupled to a single photon mode at fixed total excitation. Treating the pres
ence 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 o
f polariton condensation in optical cavities, beyond the low-density bosoni
c regime. (C) 2000 Elsevier Science Ltd. All rights reserved.