Abstract
In the limit of large field-relaxation rates as compared to the rates of collective and atomic relaxation, we model the stochastic evolution of a bistable system with the aid of the Langevin equations for atomic variables. This semiclassical approach leads to a Fokker-Planck equation for the joint probability distribution of the atomic polarization and inversion. The Monte Carlo integration scheme, consisting in construction of approximate random trajectories, enables us to evaluate numerically the adiabatic values of the output field, intensity, and intensity fluctuations as functions of time. The final model used in numerical work is equivalent to ignoring microscopic fluctuations and considering delta-correlated external fluctuations impressed on the driving field.
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