Quasi-periodically driven quantum systems

TL;DR

This paper reviews the theoretical framework for quasi-periodically driven quantum systems, extending Floquet theory and the Floquet-Magnus expansion, highlighting their potential for quantum simulations.

Contribution

It introduces generalizations of Floquet theory and the Floquet-Magnus expansion for non-periodic driving, advancing understanding of quasi-periodic quantum systems.

Findings

Quasi-periodic systems can be treated with Floquet generalizations in certain regimes.

The Floquet-Magnus expansion is extended to quasi-periodic driving.

Quasi-periodic driving shows promise for quantum simulation applications.

Abstract

Floquet theory provides rigorous foundations for the theory of periodically driven quantum systems. In the case of non-periodic driving, however, the situation is not so well understood. Here, we provide a critical review of the theoretical framework developed for quasi-periodically driven quantum systems. Although the theoretical footing is still under development, we argue that quasi-periodically driven quantum systems can be treated with generalizations of Floquet theory in suitable parameter regimes. Moreover, we provide a generalization of the Floquet-Magnus expansion and argue that quasi-periodic driving offers a promising route for quantum simulations.