The propagator formulation of the degenerate parametric oscillator

After systematically deriving general expressions for a two-time correlation function and the photon number distribution in terms of the Q-function, we analyze the squeezing spectrum and the photon number distribution of the signal mode produced by a degenerate parametric oscillator operating below threshold. The time-dependent Q-function is obtained by solving the pertinent Fokker-Planck equation applying the method of evaluating the propagator discussed in J. Math. Phys. 33 (1992) 2179.