Special lecture: Prof. Milena Grifoni

Introduction to Floquet theory

University of Regensburg
How to characterize properties of a quan-tum system subject to an intense time-periodic drive? We shall address this question within the framework of Floquet theory. According to the Floquet theorem, the solutions of the time-dependent Schrö-dinger equation display a quasi-stationary evolution, governed by quasi-energies, and a periodic part. Working in the Sambe space, it is possible to evaluate both the so-called quasi-energy spectrum and the Floquet functions without resorting to perturbation theory in the strength of the time-periodic drive or other commonly used approxim-ations. Noticeably, the quasi-energy spect-rum can be qualitatively different from the one of the undriven Hamiltonian, opening pathways to manipulate properties of quantum systems by a time-periodic drive. These concepts will be illustrated on the example of a strongly driven two-level system.