Lie algebraic approach to a nonstationary atom-cavity system

Abstract

In this work, we study the generation of photons inside an ideal cavity with resonantly oscillating boundaries in the presence of a two-level atom. We make use of Lie algebraic techniques to obtain an approximate time-evolution operator and not only evaluate the resonant and dispersive regimes but also explore different regions of parameters. We have found a very good agreement between our approximate results and those obtained by numerical means.