Quantum statistics of a superradiant laser

Abstract

The stationary behaviour and the photon statistics of a superradiant laser are investigated by solving a Fokker-Planck equation for a quantum-mechanical distribution function denned in the Hilbert space of the atomic system. The limit of validity of this Fokker-Planck equation coincides with the physical condition which distinguishes a superradiant laser from an ordinary laser,i.e. essentially the photon lifetime has to be much shorter than the coherence time of the atomic dipoles. Photon statistics can be obtained by a theorem which states a connection between the atomic distribution function and the Glauber P-function for the electromagnetic field. The limit of validity of this theorem is the superradiance limit referred to above. We solve the Fokker-Planck equation far below and above threshold, giving explicitly the P-function and discussing the photon statistics in the two cases. Atomatom and atom-field correlations are also investigated so that the limit of validity of the self-consistent field approximation can be evaluated.