Effects of quenching protocols based on parametric oscillators

Abstract

We consider the problem of understanding the basic features displayed by quantum systems described by parametric oscillators whose time-dependent frequency parameter $\omega (t)$ varies continuously during evolution so to realise quenching protocols of different types. To this scope we focus on the case where $\omega (t{)}^2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,{\omega }^2)$ plane. We derive closed form solution for the time-dependent amplitude of quasi-normal modes, which is the very fundamental dynamical object entering the description of both classical and quantum parametric oscillators, and highlight its significant characteristics for distinctive cases arising based on the driving specifics. After doing so, we provide an insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.

arXiv commentRevised version for the manuscript initially entitled: Classical and quantum analysis of the parametric oscillator with Morse-like time-dependent frequency. Overall presentation has been improved: some figures have been removed, the section with the most mathematical material now appears as Appendix, more applications of parametric oscillator systems have been mentioned in the Introduction

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