High-order Harmonic Generation and Dynamic Localization in a driven two-level system, a non-perturbative solution using the Floquet-Green formalism

TL;DR

This paper presents an exact non-perturbative analysis of a driven two-level quantum system using Floquet-Green formalism, revealing insights into high-order harmonic generation and dynamic localization phenomena.

Contribution

It derives exact quasi-energy expressions and Floquet states for a driven two-level system, enabling detailed study of non-perturbative effects.

Findings

Identification of avoided crossing structures in quasi-energies

Interpretation of avoided crossings as multi-photon resonances

Demonstration of dynamic localization and high-harmonic generation in non-perturbative regime

Abstract

We apply the Floquet-Green operator formalism to the case of a harmonically-driven two-level system. We derive exact expressions for the quasi-energies and the components of the Floquet eigenstates with the use of continued fractions. We study the avoided crossings structure of the quasi-energies as a function of the strength of the driving field and give an interpretation in terms of resonant multi-photon processes. From the Floquet eigenstates we obtain the time-evolution operator. Using this operator we study Dynamic Localization and High-order Harmonic Generation in the non-perturbative regime.