Time evolution of a two-atom dressed entangled state in a cavity

TL;DR

This paper investigates how two dressed atoms in a cavity evolve over time, revealing dissipation in large cavities and oscillations in small ones, while also analyzing their entanglement dynamics through von Neumann entropy.

Contribution

It provides a detailed analysis of the time evolution and entanglement behavior of two dressed atoms in different cavity sizes, highlighting the invariance of entropy over time.

Findings

Large cavities lead to dissipation and decay.

Small cavities cause oscillatory, non-decaying dynamics.

Entanglement entropy remains constant regardless of cavity size or time.

Abstract

We study the time evolution of superposition of product states of two dressed atoms in a spherical cavity in the extreme situations of an arbitrarily large cavity (free space) and of a small one. In the large-cavity case, the system dissipates, whereas, for the small finite cavity, the system evolves in an oscillating way and never completely decays. We also compute the von Neumann entropy for such a system, a measurement of the degree of entanglement of the two atoms, as the superposed state evolves in time. We find that this entropy does not depend on time, nor on the size of the cavity.