Stochastic-master-equation description of an optical bistability: A comparison with the microscopic theory

Abstract

We consider a gas of homogeneously broadened two-level atoms in a Fabry-Perot cavity injected with a coherent resonant electric field. Adopting a macroscopic birth-death description, we construct a stochastic master equation for the output intensity distribution. From this starting point we find the steady-state distribution and show it to be bimodal in the region of the optical bistability. We compare our results for the mean and variance with the microscopic results of Bonifacio, Gronchi, and Lugiato as a test of the stochastic-master-equation approach.