Quantum theory of an atomic parametric oscillator

We present a quantum theory of an atomic parametric oscillator which describes a gas of weakly interacting trapped bosons. The particles are assumed to be confined in a damped atomic cavity pumped by a coherent matter beam. We consider the three trapped levels which are the pumped and two damped modes. The system is described by a Fokker-Planck equation (FPE) for the quasi-distribution function in the complex P-representation for the density operator. Using a known steady-state solution of the FPE we derive the bason number distribution function. On the basis of an exact treatment we investigate the quantum behavior of the device, especially in the critical region. As a result, a quantum noise-induced effect is revealed. We suggest to use the device as a correlated matter waves generator. (C) 1997 Published by Elsevier Science B.V.