Dynamics of Atom-Field Entanglement from Exact Solutions: Towards Strong Coupling and Non-Markovian Regimes

TL;DR

This paper provides exact solutions for the time evolution of atom-field entanglement in various regimes, including strong coupling and non-Markovian dynamics, extending beyond traditional approximations.

Contribution

It introduces exact analytical solutions for atom-field entanglement dynamics in complex multi-mode and infinite-mode systems, capturing non-Markovian effects.

Findings

Exact solutions for bipartite entanglement in multi-mode systems

Demonstration of non-Markovian dynamics in atom-field interactions

Analysis of strong coupling regimes beyond Markovian approximation

Abstract

We examine the dynamics of bipartite entanglement between a two-level atom and the electromagnetic field. We treat the Jaynes-Cummings model with a single field mode and examine in detail the exact time evolution of entanglement, including cases where the atomic state is initially mixed and the atomic transition is detuned from resonance. We then explore the effects of other nearby modes by calculating the exact time evolution of entanglement in more complex systems with two, three, and five field modes. For these cases we can obtain exact solutions which include the strong coupling regimes. Finally, we consider the entanglement of a two-level atom with the infinite collection of modes present in the intracavity field of a Fabre-Perot cavity. In contrast to the usual treatment of atom-field interactions with a continuum of modes using the Born-Markov approximation, our treatment in all cases describes the full non-Markovian dynamics of the atomic subsystem. Only when an analytic expression for the infinite mode case is desired do we need to make a weak coupling assumption which at long times approximates Markovian dynamics.