Multipartite entanglement dynamics in a cavity

TL;DR

This paper investigates the complex dynamics of multipartite and bipartite entanglement in a three-atom system coupled to a cavity, revealing bounds and critical interaction values affecting entanglement evolution.

Contribution

It introduces two Hamiltonians for a three-atom system interacting with a cavity and analyzes their impact on entanglement bounds and dynamics.

Findings

An upper bound for concurrence as a function of purity was established.

A lower bound for the homogeneous case was identified.

Critical interaction values lead to complex entanglement dynamics.

Abstract

We study the dynamics of two kinds of entanglement, and there interplay. On one hand, the intrinsic entanglement within a central system composed by three two level atoms, and measured by multipartite concurrence, on the other, the entanglement between the central system and a cavity, acting as an environment, and measured with purity. Using dipole-dipole and Ising interactions between atoms we propose two Hamiltonians, a homogeneous and a quasi-homogeneous one. We find an upper bound for concurrence as a function of purity, associated to the evolution of the $W$ state. A lower bound is also observed for the homogeneous case. In both situations, we show the existence of critical values of the interaction, for which the dynamics of entanglement seem complex.