Entanglement of a two-particle Gaussian state interacting with a heat bath

TL;DR

This paper investigates how a thermal environment affects entanglement in a bipartite Gaussian state, revealing oscillations and long-term persistence of entanglement under weak damping conditions.

Contribution

It derives a pre-Lindblad master equation for the system and analyzes entanglement dynamics, highlighting differences between strong and weak damping regimes.

Findings

Entanglement loss is similar to free evolution under strong damping.

Weak damping causes entanglement to oscillate and stabilize at a nonzero value.

The study provides insights into entanglement behavior in thermal environments.

Abstract

The effect of a thermal reservoir is investigated on a bipartite Gaussian state. We derive a pre-Lindblad master equation in the non-rotating wave approximation for the system. We then solve the master equation for a bipartite harmonic oscillator Hamiltonian with entangled initial state. We show that for strong damping the loss of entanglement is the same as for freely evolving particles. However, if the damping is small, the entanglement is shown to oscillate and eventually tend to a constant nonzero value.