Non-Markovian Entanglement Dynamics of Two Qubits Interacting with a Common Electromagnetic Field

TL;DR

This paper investigates the non-Markovian entanglement dynamics of two spatially separated qubits interacting with a common electromagnetic field, revealing differences from Markovian predictions and analyzing decoherence effects.

Contribution

It provides a detailed analysis of non-Markovian entanglement evolution without relying on the Born or Markov approximations, highlighting qualitative differences from Markovian models.

Findings

No sudden death of entanglement for Class A states under non-Markovian dynamics.

Entanglement behavior differs significantly between state classes and approximation methods.

Decoherence characteristics are analyzed for the two-qubit system.

Abstract

We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance $r$ and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption but no Born or Markov approximation. We write the evolution equations of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. We study two classes of states in detail: Class A is a one parameter family of states which are the superposition of the highest energy and lowest energy states, and Class B states which are the linear combinations of the symmetric and the antisymmetric Bell states. Our results for an initial Bell state are similar to those obtained before for the same model derived under the Born-Markov approximation. However, in the Class A states the behavior is qualitatively different: under the non-Markovian evolution we do not see sudden death of quantum entanglement and subsequent revivals, except when the qubits are sufficiently far apart. We provide explanations for such differences of behavior both between these two classes of states and between the predictions from the Markov and non-Markovian dynamics. We also study the decoherence of this two-qubit system.