Parametric oscillator in a Kerr medium: evolution of coherent states

TL;DR

This paper investigates how coherent states evolve over time in a system combining a parametric oscillator with a Kerr medium, revealing squeezing effects and validating approximations with numerical results.

Contribution

It introduces an analytical approach using Lie algebra approximations to study the evolution of coherent states in a nonlinear Kerr medium with a parametric oscillator.

Findings

The evolution operator acts like a squeezing operator.

Approximate results agree well with numerical calculations.

The study characterizes the probability amplitude and autocorrelation function.

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.