Isotropic and squeezed colored pump noise effects on the degenerate parametric oscillator

Abstract

The degenerate parametric oscillator above threshold is studied with phenomenological stochastic colored ~nonwhite! pump noise for arbitrary pump to subharmonic relaxation rate. The current experimental limits of large intracavity threshold photon numbers ~very small quantum noise! are considered, allowing for a semiclassical treatment of the system dynamics. A comparison between the effects of isotropic and squeezed pump noise on the internal transient and steady-state fluctuations is presented by simulation of the nonlinear semiclassical stochastic Langevin equations in the Wigner quadrature representation. It is found that the transient squeezing for the system starting in the unstable steady state ~the vacuum! is not degraded by stochastic pump noise. A damped oscillatory behavior of the noise levels ~periodic exchange of fluctuations between the squeezed quadrature of the signal and the pump! is observed for large damping of the signal in the turn on of pump depletion. Finally, it is shown that the limited squeezing above threshold in the steady state (50%) due to pump depletion can be enhanced if squeezed stochastic noise with sufficient significant spectral components ~broadband squeezing! is fed to the pump. The above-threshold steady-state squeezing has been calculated analytically from the linearized stochastic equations and the effects of the time scale associated to the relaxation of the pump noise ~the noise correlation time! compared to the dissipative time scale of the system and the pump to subharmonic loss ratio are presented. @S1050-2947~96!03609-8#