Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments

TL;DR

This paper investigates how quantum entanglement between two continuous variable systems evolves over time in non-Markovian thermal environments, considering different coupling scenarios and initial states.

Contribution

It derives non-Markovian master equations for two models of harmonic oscillators interacting with thermal baths, highlighting the impact of environment and initial conditions on entanglement dynamics.

Findings

Entanglement dynamics depend on initial states and interactions.

Common vs. independent reservoirs influence entanglement evolution.

Non-Markovian effects significantly affect entanglement decay and revival.

Abstract

We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for the bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.