Parametric oscillator in a Kerr medium: evolution of coherent states

Abstract

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.

11 pages, 3 figures

References in corpus (2)

• Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations
• Generation of squeezed Schrödinger cats in a tunable cavity filled with a Kerr medium

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• Generation of squeezed Schrödinger cats in a tunable cavity filled with a Kerr medium
• Coherent states of parametric oscillators in the probability representation of quantum mechanics
• Vacuum radiation versus shortcuts to adiabaticity
• Quantum dynamics of a driven parametric oscillator in a Kerr medium
• Gaussian approximation and its corrections for driven dissipative Kerr model