Temporal evolution of a forced optomechanical system with linear and quadratic field -- mechanical oscillator couplings

TL;DR

This paper derives the exact and approximate time evolution operators for a forced optomechanical system with linear and quadratic couplings, using Lie algebraic methods, and validates results with numerical simulations.

Contribution

It introduces a Lie algebraic approach to analytically solve the dynamics of a complex optomechanical system with both linear and quadratic couplings.

Findings

Exact solution for non-driven system's evolution operator.

Approximate solution for forced system's evolution operator.

Good agreement between analytical and numerical results.

Abstract

In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a non-driven system and find its exact time evolution operator, secondly we consider the case of a forced system whose time evolution operator is obtained in an approximate form. We confront our analytical results with a numerical simulation and find a good agreement between them.