Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system

TL;DR

This paper investigates how driving and finite environment size influence non-Markovian effects in an open quantum system, revealing that information backflow depends on driving and environment parameters, with non-monotonic dependence on environment size.

Contribution

It introduces a model to quantify non-Markovianity in a driven qubit with a finite environment, analyzing how driving, environment size, and coupling affect memory effects.

Findings

Information backflow occurs only with driving.

Non-Markovianity depends on the ratio of driving amplitude to coupling.

Non-Markovianity does not decrease monotonically with environment size.

Abstract

We study non-Markovian effects present in a driven qubit coupled to a finite environment using a recently proposed model developed in the context of calorimetric measurements of open quantum systems. To quantify the degree of non-Markovianity we use the Breuer-Laine-Piilo (BLP) measure [Breuer \textit{et al.}, Phys. Rev. Lett. \textbf{103}, 210401 (2009)]. We show that information backflow only occurs in the case of driving in which case we investigate the dependence of memory effects on the environment size, driving amplitude and coupling to the environment. We show that the degree of non-Markovianity strongly depends on the ratio between the driving amplitude and the coupling strength. We also show that the degree of non-Markovianity does not decrease monotonically as a function of the environment size.