System-environment correlations and Non-Markovian dynamics

TL;DR

This paper investigates the dynamics of a dephasing quantum system interacting with a harmonic oscillator environment, exploring the relationship between non-Markovian behavior and system-environment correlations, including classical and quantum entanglement.

Contribution

It provides a detailed analysis of system-environment correlations in non-Markovian quantum dynamics, revealing their potential classical nature and complex relation to non-Markovianity.

Findings

Non-Markovian dynamics can occur with a loss of system-environment correlations.

System-environment entanglement may be present or absent depending on initial conditions.

No clear link between quantum correlations and non-Markovianity was observed.

Abstract

We determine the total state dynamics of a dephasing open quantum system using the standard environment of harmonic oscillators. Of particular interest are random unitary approaches to the same reduced dynamics and system-environment correlations in the full model. Concentrating on a model with an at times negative dephasing rate, the issue of "non-Markovianity" will also be addressed. Crucially, given the quantum environment, the appearance of non-Markovian dynamics turns out to be accompanied by a loss of system-environment correlations. Depending on the initial purity of the qubit state, these system-environment correlations may be purely classical over the whole relevant time scale, or there may be intervals of genuine system-environment entanglement. In the latter case, we see no obvious relation between the build-up or decay of these quantum correlations and "Non-Markovianity".