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

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/ω m , is not negligible compared to one, i.e., the system operates in the strong-coupling regime. 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. In contrast to other works, our approach does not use the standard linearized description in the optomechanical interaction. Therefore, highly non-classical (non-Gaussian) states of light emerge during the time evolution.

Linear entropy in the atom-field interaction at finite temperature

“…+ ( Ĝ|e g| + H.c.), (28) where we have not explicitly written the term Ĝ because when the atomic trace is taken it disappears. Applying the superoperator e RΓ t and performing the atomic trace we arrive at the simple result…”

“…We have studied the atom-field interaction in the strong coupling regime [28] at finite temperature when the field is initially in a coherent state and in the dispersive regime. By using superoperator techniques, we manage to solve the master equation for this system and have calculated the linear entropy.…”