Hidden time-nonlocal Floquet symmetries

TL;DR

This paper reveals a hidden time-nonlocal Floquet symmetry in a driven two-level system, explaining exact quasienergy crossings and providing a general numerical scheme applicable beyond the specific model.

Contribution

It introduces a new hidden symmetry in Floquet systems, offers a constructive proof, and develops a general numerical method for models beyond two-level systems.

Findings

Exact quasienergy crossings occur at integer detuning multiples.

Hidden time-nonlocal parity classifies Floquet modes as even or odd.

Numerical scheme applicable to broader models beyond the two-level system.

Abstract

We investigate the Floquet spectrum of a detuned, driven two-level system and show that it exhibits exact quasienergy crossings when the detuning is an integer multiple of the energy quantum of the driving field. This behavior can be explained by a hidden time-nonlocal parity, which allows the Floquet modes to be classified as even or odd. Then a generic feature is the emergence of exact crossings between quasienergies of different parity. A constructive proof of the existence of the symmetry is based on a scalar recurrence relation. Moreover, we present a general scheme for its numerical computation, which can be applied to models beyond the two-level system. Analytical results are illustrated with numerical data.