Quantum non-Markovianity induced by Anderson localization

TL;DR

This paper demonstrates that Anderson localization in a disordered coupled-cavity array induces non-Markovian dynamics in a quantum emitter, linking localization to quantum information backflow.

Contribution

It establishes a direct relationship between Anderson localization and quantum non-Markovianity in atom-lattice interactions, supported by a phenomenological model.

Findings

Disorder-induced localization leads to non-Markovian atomic dynamics.

A measure of non-Markovianity correlates with Anderson localization.

A simple model captures the average non-Markovianity behavior.

Abstract

As discovered by P. W. Anderson, excitations do not propagate freely in a disordered lattice, but, due to destructive interference, they localise. As a consequence when an atom interacts with a disordered lattice one indeed observes, a non-trivial excitation exchange between atom and lattice. Such non-trivial atomic dynamics will in general be characterised also by a non-trivial quantum information backflow, a clear signature of non-Markovian dynamics. To investigate the above scenario we consider a quantum emitter, or atom, weakly coupled to a uniform coupled-cavity array (CCA). If initially excited, in the absence of disorder, the emitter undergoes a Markovian spontaneous emission by releasing all its excitation into the CCA (initially in its vacuum state). By introducing static disorder in the CCA the field normal modes become Anderson-localized, giving rise to a non-Markovian atomic dynamics. We show the existence of a functional relationship between a rigorous measure of quantum non-Markovianity and the CCA localization. We furthermore show that the average non-Markovianity of the atomic dynamics is well-described by a phenomenological model in which the atom is coupled, at the same time, to a single mode and to a standard - Markovian - dissipative bath.