Quantum Noise. XIII. Six-Classical-Variable Description of Quantum Laser Fluctuations

An exact $c$-number generalized Fokker-Planck equation is derived for six noncommuting variables: the field variables, atomic populations, and atomic polarization of a laser model treated extensively by Lax. Langevin procedures yield the correct Fokker-Planck terms. Adiabatic eliminations are performed on the classical Markoff process given by the Fokker-Planck equation to compare with previous results. It is found that higher-order diffusion coefficients influence the second-order ones slightly during adiabatic elimination.