Statistics of a parametric oscillator in a thermal reservoir

A parametric Bose oscillator evolving from a state in the form of a signal-noise superposition is considered. The region of values of its frequency, the temperature, the optical pumping, and the time for which the occupation numbers satisfy sub-Poisson statistics is found. It is noted that the sub-Poisson effect is delayed by thermal fluctuations in the long-wavelength region and suppressed by quantum fluctuations in the short-wavelength region, the suppression taking the form of a frequency threshold condition at low temperatures