Time evolution of a superposition of dressed oscillator states in a cavity

TL;DR

This paper investigates the nonperturbative time evolution of a superposition of dressed harmonic oscillator states within a cavity, revealing dissipation in large cavities and oscillatory behavior in small ones, with improved theoretical accuracy.

Contribution

It introduces a nonperturbative analysis using renormalized coordinates and dressed states to study superposition dynamics in a cavity, surpassing previous perturbative methods.

Findings

Dissipation dominates in large cavities for both coupling regimes.

Small cavities exhibit oscillatory, non-dissipative behavior.

Results improve upon earlier perturbative approaches.

Abstract

Using the formalism of {\it renormalized} coordinates and \textit{dressed} states introduced in previous publications, we perform a nonperturbative study of the time evolution of a superposition of two states, the ground state and the first excited level of a harmonic oscillator, the system being confined in a perfectly reflecting cavity of radius $R$. For $R\to\infty$, we find dissipation with dominance of the interference terms of the density matrix, in both weak- and strong-coupling regimes. For small values of $R$ all elements of the density matrix present an oscillatory behavior as times goes on and the system is not dissipative. In both cases, we obtain improved theoretical results with respect to those coming from perturbation theory.