Memory effects in a quasi-periodic Fermi lattice

TL;DR

This paper explores how a quasi-periodic Fermi lattice exhibits memory effects in its dynamics, especially in the localized phase, which acts as a controllable non-Markovian environment for an impurity atom.

Contribution

It introduces a protocol to study impurity dynamics in a quasi-periodic Fermi system and demonstrates the presence of strong, stable memory effects in the localized phase.

Findings

Localized phase shows strong non-Markovian behavior.

Memory effects are stable and controllable.

The environment can be tuned to exhibit Markovian or non-Markovian dynamics.

Abstract

We investigate a system of fermions trapped in a quasi-periodic potential from an open quantum system theory perspective, designing a protocol in which an impurity atom (a two level system) is coupled to a trapped fermionic cloud described by the non-interacting Aubry-Andr\'e model. The Fermi system is prepared in a charge density wave state before it starts its relaxation. In this work we focus our attention on the time evolution of the impurity in such an out of equilibrium environment, and study whether the induced dynamics can be classified as Markovian or non-Markovian. We find how the localised phase of the Aubry-Andr\'{e} model displays evidence of strong and stable memory effects and can be considered as a controllable and robust non-Markovian environment.