Quantum dynamics of a driven parametric oscillator in a Kerr medium

Abstract

AbstractIn 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 $$t\rightarrow \int _0^t dt'\,1/m(t')$$ t → ∫ 0 t d t ′ 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 $$\chi $$ χ , 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.