Exact steady-state Wigner function for a nondegenerate parametric oscillator - art. no. 015801

We consider the model of a nondegenerate parametric oscillator, in the adia batic limit of strongly damped pump mode, and find an exact analytic soluti on for the joint two-mode Wigner function in the steady-state regime. The o ne-mode Wigner functions for the individual signal and idler modes are deri ved as well. This gives an explicit and complete phase-space representation of this two-mode nonequilibrium quantum system. Simple examples are given illustrating the phase-space images of optical bistability and the phase di ffusion effect.