Exact Results for Photon Statistics for a Model of Optical Bistability

Abstract

Optical bistability can be viewed either as a first- or second-order phase transition depending on whether single atom effects are included (first-order) or excluded (second-order)^1,2. In a purely cooperative system it has recently been shown³’⁴ that the density matrix governing the evolution of the cooperative atomic system has a nontrivial steady state solution from which atomic correlation functions of arbitrary order are immediately obtained. It is our intention here to use these to generate the equal time photon distribution function p_n for the light emerging from the cavity. We believe this complements earlier studies of similar systems where attention w s focused either on spectral properties f the emitted light^5,6, or on its correlation function g⁽²⁾(τ = O)⁴.