Schr\"odinger-Koopman quasienergy states of quantum systems driven by a classical flow

TL;DR

This paper introduces a generalized quasienergy framework for quantum systems driven by classical flows, linking classical dynamical properties to quantum behavior, with applications in quantum control and information.

Contribution

It develops the Schr"odinger-Koopman quasienergy approach, extending Floquet theory to systems influenced by classical dynamical systems, including chaotic maps.

Findings

Classical flow properties affect quantum quasienergy spectra.

The approach applies to systems with classical chaos and regularity.

Demonstrated with kicked spin ensembles driven by Arnold's cat map and Chirikov map.

Abstract

We study the properties of the quasienergy states of a quantum system driven by a classical dynamical system. The quasienergies are defined in a same manner as in light-matter interaction but where the Floquet approach is generalized by the use of the Koopman approach of dynamical systems. We show how the properties of the classical flow (fixed and cyclic points, ergodicity, chaos) influence the driven quantum system. This approach of the Schr\"odinger-Koopman quasienergies can be applied to quantum control, quantum information in presence of noises, and dynamics of mixed classical-quantum systems. We treat the example of a kicked spin ensemble where the kick modulation is governed by discrete classical flows as the Arnold's cat map and the Chirikov standard map.