Asymptotic Discord and Entanglement of Non-Resonant Harmonic Oscillators in an Equilibrium Environment

TL;DR

This paper provides exact analytical formulas for quantum correlations, including discord and entanglement, between non-resonant harmonic oscillators in a common environment, revealing complex behaviors across different dissipation regimes.

Contribution

It derives analytical formulas for Gaussian stationary states of non-resonant oscillators in a bath, analyzing quantum discord and entanglement in various dissipation regimes.

Findings

Stationary entanglement exists only within a finite frequency band.

Strong dissipation can induce entanglement through the environment.

Robust entanglement observed between detuned oscillators at low temperature.

Abstract

In this work, we calculate the exact asymptotic quantum correlations between two interacting non-resonant harmonic oscillators in a common Ohmic bath. We derive \emph{analytical formulas} for the covariances, fully describing any Gaussian stationary state of the system, and use them to study discord and entanglement in the strong and weak dissipation regimes. We discuss the rich structure of the discord of the stationary separable states arising in the strong dissipation regime. Also under strong dissipation, when the modes are not mechanically coupled, these may entangle only through their interaction with the \emph{common} environment. Interestingly enough, this stationary entanglement is only present within a \emph{finite band of frequencies} and increases with the dissipation rate. In addition, robust entanglement between \emph{detuned} oscillators is observed at low temperature.