Linear-response theory in Floquet systems

TL;DR

This paper develops a linear response theory for Floquet systems, enabling analysis of their spectral properties and photoemission spectra under time-periodic driving, with applications to Floquet engineering.

Contribution

It introduces the first comprehensive linear response framework for Floquet many-body systems, extending equilibrium concepts to nonequilibrium periodic Hamiltonians.

Findings

Derived the Floquet analogue of Fermi's Golden Rule.

Established the positivity of the spectral function in Floquet systems.

Analyzed how Floquet engineering controls photoemission spectra.

Abstract

Nonequilibrium quantum physics greatly simplifies in the case of time-periodic Hamiltonians, since Floquet theory provides an analogue to Bloch's theorem in the time domain. Still, the formal properties of Floquet many-body theory remain underexplored. Here, we develop linear response theory for Floquet systems, in the sense that we have a time-periodic potential of arbitrary strength and a perturbatively small but non-periodic probing field. As an application, we derive the analogy of Fermi's Golden Rule and the photoemission spectrum of a many-electron system. As in the equilibrium case, the latter is related to the spectral function which is positive definite. We also analyze the parameter dependence of the controllable photoemission spectra by virtue of Floquet engineering.