Asymptotic Floquet states of non-Markovian systems

TL;DR

This paper introduces a method to determine the long-term behavior of non-Markovian open quantum systems with periodic driving by embedding them into an enlarged state space and applying Floquet analysis.

Contribution

It develops a novel Floquet-based approach for non-Markovian systems using an enlarged state space, enabling the calculation of asymptotic states beyond traditional Floquet theory.

Findings

Successfully applied to a modulated quantum random walk model.

Provides a way to estimate relaxation times via spectral gap analysis.

Extends Floquet theory to non-Markovian dynamics with memory effects.

Abstract

We propose a method to find asymptotic states of a class of periodically modulated open systems which are outside the range of validity of the Floquet theory due to the presence of memory effects. The method is based on a Floquet treatment of the time-local, memoryless dynamics taking place in a minimally enlarged state space where the original system is coupled to auxiliary -- typically non-physical -- variables. A projection of the Floquet solution into the physical subspace returns the sought asymptotic state of the system. The spectral gap of the Floquet propagator acting in the enlarged state space can be used to estimate the relaxation time. We illustrate the method with a modulated version of quantum random walk model.