Condensation of photons coupled to a Dicke field in an optical microcavity

Motivated by recent experiments reporting Bose-Einstein condensation of light coupled to incoherent dye molecules in a microcavity, we show that due to a dimensionality mismatch between the two-dimensional cavity photons and the three-dimensional arrangement of molecules, the system permits superfluid regimes where the relevant molecular degrees of freedom are collective Dicke states rather than individual excitations. For sufficiently high dye concentration, Dicke states become robust against local decoherence. In the limit when all dye molecules become excited, this system also shows Mott-Hubbard physics, despite the absence of an underlying lattice.