### Abstract:

We obtain stochastic di®erential equations for the nondegenerate parametric
oscillator with the cavity modes driven by coherent light and coupled to a
two-mode squeezed vacuum reservoir. With the aid of these equations, we
calculate the quadrature variance and the squeezing spectrum. It is found
that the two-mode squeezed vacuum increases the degree of squeezing. It
is also found that for ! = 0 the noise in the plus quadrature is completely
suppressed. However, the two-mode driving light has no e®ect on the
squeezing properties of the cavity modes.
On the other hand, using the solutions of the stochastic di®erential
equations, we calculate the mean and the variance of the photon number.
It turns out that the two-mode driving light and the two-mode squeezed
vacuum increase the mean and the variance of the photon number. Furthermore,
employing the same solutions, we also obtain the antinormally ordered
characteristic function de¯ned in the Heisenberg picture. With the help
of the resulting characteristic function, we determine the Q function which
is then used to calculate the photon number distribution. Moreover, we
calculate the mean, the variance, the photon number distribution for the
number of photon pairs, in the absence of the two-mode driving light