Steady state of periodically driven quantum systems

TL;DR

This paper investigates the steady states of periodically driven open quantum systems, establishing general conditions for thermalization and revealing that high-temperature NESS follow a uniform distribution, supported by theoretical and numerical analysis.

Contribution

It extends Floquet scattering theory to characterize NESS in generic driven quantum systems beyond common approximations.

Findings

High-temperature NESS follow a uniform distribution.

Derived general Floquet thermalization conditions.

Numerical results support theoretical predictions.

Abstract

Periodic driving is used to steer physical systems to unique stationary states or nonequilibrium steady states (NESS), producing enhanced properties inaccessible to non-driven systems. For open quantum systems, characterizing the NESS is challenging and existing results are generally limited to specific types of driving and the Born-Markov approximation. Here we go beyond these limits by studying a generic periodically driven $ N$-level quantum system interacting with a low-density thermal gas. Exploiting the framework of Floquet scattering theory, we establish general Floquet thermalization conditions constraining the nature of the NESS and the transition rates. Moreover, we examine theoretically the structure of the NESS in the high temperature limit, and find out that the NESS complies, rather surprisingly, with an uniform probability distribution (predicted by the Boltzmann law) for any driving. Numerical calculations illustrate our theoretical elaborations for a simple toy model.