Parametric oscillator in a Kerr medium: evolution of coherent states

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time independent part of the Hamiltonian. We approximate the interaction picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze the probability amplitude and the auto correlation function for different Hamiltonian parameters and we find a very good agreement between our approximate results and converged numerical calculations.Comment: 11 pages, 3 figure

Approximate evolution for a system composed by two coupled Jaynes-Cummings Hamiltonians

In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our approximations contrasting our analytical results with those obtained by purely numerical methods.Comment: 15 pages, 3 figures, 1 tabl