Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their trivial mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the quantum anharmonic oscillator. The photon statistics at the crossover are different in the high-temperature and low-temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects.