Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains

TL;DR

This paper develops a formalism for analyzing the effects of noise on periodically driven quantum systems, particularly focusing on the robustness of Floquet topological states against noise-induced decoherence.

Contribution

It introduces a noise-averaged Floquet superoperator framework that generalizes Floquet theory to noisy systems, enabling analysis of decoherence and topological state decay.

Findings

Eigenvectors of the Floquet superoperator describe decoherence effects.

The formalism confirms noise-induced decay of topologically protected states.

Application to noisy Floquet chains illustrates the formalism's effectiveness.

Abstract

Much recent experimental effort has focused on the realization of exotic quantum states and dynamics predicted to occur in periodically driven systems. But how robust are the sought-after features, such as Floquet topological surface states, against unavoidable imperfections in the periodic driving? In this work, we address this question in a broader context and study the dynamics of quantum systems subject to noise with periodically recurring statistics. We show that the stroboscopic time evolution of such systems is described by a noise-averaged Floquet superoperator. The eigenvectors and -values of this superoperator generalize the familiar concepts of Floquet states and quasienergies and allow us to describe decoherence due to noise efficiently. Applying the general formalism to the example of a noisy Floquet topological chain, we re-derive and corroborate our recent findings on the noise-induced decay of topologically protected end states. These results follow directly from an expansion of the end state in eigenvectors of the Floquet superoperator.