Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

TL;DR

This paper provides exact solutions for two interacting atoms of different species in a cavity, analyzing entanglement and decoherence dynamics through explicit eigenstates and functions.

Contribution

It introduces a new invariant to solve the model exactly, unifying various existing models and deriving explicit time-dependent entanglement measures.

Findings

Explicit eigenvalues and eigenfunctions obtained

Closed-form expressions for concurrence and purity

Analysis of entanglement and decoherence behavior

Abstract

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.