Parametric Oscillation with Squeezed Vacuum Reservoirs
  Employing the quantum Hamiltonian describing the interaction of two-mode light (signal-idler modes) generated by a nondegenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master equation. The corresponding Fokker-Planck equation for the Q-function is then solved employing a propagator method developed in Ref. \cite{1}. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal-idler modes are in squeezed states and the squeezing occurs in the first quadrature. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in the first quadrature can be achieved. 
Alem Mebrahtu