Evolution of a Nonlinear Coherent State in a Parametric Oscillator in Presence of the Kerr Medium

In this paper, the temporal evolution of the nonlinear coherent states in a parametric oscillator in the presence of a Kerr medium is investigated. For this purpose, the Hamiltonian of the system is written in the interaction picture and as a combination of time-independent operators with time - dependent coefficients using an approximation method. Then, the temporal evolution of a nonlinear coherent state is obtained by exerting the corresponding time-evolution operator. In addition, the Mandel parameter, the auto - correlation function and the Husimi-Q distribution function of the time-dependent nonlinear coherent states in the parametric oscillator in a Kerr Medium are studied and analyzed.