Temporal evolution of a driven optomechanical system in the strong coupling regime

TL;DR

This paper develops an analytical method to describe the time evolution of a driven optomechanical system in the strong coupling regime, using Lie algebraic techniques and approximations validated by numerical comparisons.

Contribution

It introduces a novel analytical approach for the dynamics of driven optomechanical systems in the strong coupling regime, incorporating forcing effects and approximations validated by numerical results.

Findings

Analytical time-evolution operator derived for strong coupling regime

Approximation of exponential operators using initial coherent states

Excellent agreement between analytical and numerical results

Abstract

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared to one. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement.