An exact Markovian decoherence dynamics of two interacting harmonic oscillators coupled to a bosonic heat bath

TL;DR

This paper provides an exact analytical solution for the Markovian decoherence dynamics of two coupled harmonic oscillators interacting with a thermal bath, analyzing entanglement behavior over time and under various conditions.

Contribution

It introduces a precise solution to the Hu-Paz-Zhang master equation for a two-oscillator system with a common thermal bath, revealing detailed entanglement dynamics and stability conditions.

Findings

Undamped dynamics in the relative coordinate due to decoupling.

Periodic entanglement-disentanglement behavior under certain conditions.

Entanglement can be maintained at high temperatures with negative coupling near stability bounds.

Abstract

We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise Markovian limit for a system of two harmonically coupled harmonic oscillators interacting with a common thermal bath of harmonic oscillators. The thermal bath is initially considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz-Drude spectral density. In the examined system, couplings between the two harmonic oscillators and the environment ensure a complete decoupling of the center-of-mass and relative degrees of freedom, resulting in undamped dynamics in the relative coordinate. The exact time evolution is used to analyze the system's entanglement dynamics, quantified through logarithmic negativity and quantum mutual information, while ensuring the positivity of the density operator to confirm the physical validity of the results. We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore, numerical simulations reveal that for negative values of the direct coupling between the oscillators, which are sufficiently close to a critical lower bound beyond which the system becomes unstable, the system can maintain entanglement across a broad temperature range and for arbitrarily long durations.