Quantum theory of the two-photon laser

We start from a master equation for the density operator of the atoms and the field mode, and apply the operator method of adiabatic elimination of the atomic variables, recently developed by Haake and Lewenstein for the usual single mode laser, to the case of a degenerate two-photon laser. A Fokker-Planck equation for the Wigner distribution function of the lightfield and its steady state solution are derived. With a Gaussian approximation to the solution, analytical and numerical results on the photon statistics are calculated.