Quantum noise IX: Quantum Fokker-Planck solution for laser noise

A dynamic correspondence is set up between the density matrix of the electromagnetic field and an associated classical function. Means of one and two time quantum operators are shown to be obtainable from the corresponding averages of the associated classical random problem. When all atomic response rates are fast compared to photon rates, the equation of motion is obtained for the field density matrix. The associated classical problem is shown to obey a Fokker-Planck equation. Over a broad region that includes the threshold region, the Fokker-Planck equation is reduced to that for the rotating-wave van der Pol oscillator for which exact numerical solutions have been previously obtained by Hempstead and Lax.