Parametric Oscillation With Two-mode Squeezed Vacuum And Coherent Light

We obtain stochastic di®erential equations for the nondegenerate parametricrnoscillator with the cavity modes driven by coherent light and coupled to arntwo-mode squeezed vacuum reservoir. With the aid of these equations, werncalculate the quadrature variance and the squeezing spectrum. It is foundrnthat the two-mode squeezed vacuum increases the degree of squeezing. Itrnis also found that for ! = 0 the noise in the plus quadrature is completelyrnsuppressed. However, the two-mode driving light has no e®ect on thernsqueezing properties of the cavity modes.rnOn the other hand, using the solutions of the stochastic di®erentialrnequations, we calculate the mean and the variance of the photon number.rnIt turns out that the two-mode driving light and the two-mode squeezedrnvacuum increase the mean and the variance of the photon number. Furthermore,rnemploying the same solutions, we also obtain the antinormally orderedrncharacteristic function de¯ned in the Heisenberg picture. With the helprnof the resulting characteristic function, we determine the Q function whichrnis then used to calculate the photon number distribution. Moreover, werncalculate the mean, the variance, the photon number distribution for thernnumber of photon pairs, in the absence of the two-mode driving light

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