Quantum dynamics of a driven parametric oscillator in a Kerr medium

In this paper, we first analyze a parametric oscillator with both mass and frequency time-dependent. We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and time-dependent frequency followed by a time transformation t -> integral(t)(0) dt' 1/m(t'). Then we proceed by investigating the quantum dynamics of a parametric oscillator with unit mass and time-dependent frequency in a Kerr medium under the influence of a time-dependent force along the motion of the oscillator. The quantum dynamics of the time-dependent oscillator is analyzed from both analytical and numerical points of view in two main regimes: (i) small Kerr parameter chi, and (ii) small confinement parameter k. In the following, to investigate the characteristics and statistical properties of the generated states, we calculate the autocorrelation function, the Mandel Q parameter, and the Husimi Q-function.

Automated summary

In this paper, we analyze a parametric oscillator with both mass and frequency time-dependent, and show that its evolution operator can be obtained from another parametric oscillator with constant mass and time-dependent frequency followed by a time transformation. We then investigate the quantum dynamics of a parametric oscillator with unit mass and time-dependent frequency in a Kerr medium under the influence of a time-dependent force. The characteristics and statistical properties of the generated states are studied by calculating the autocorrelation function, the Mandel Q parameter, and the Husimi Q-function.