Floquet resonances close to the adiabatic limit and the effect of dissipation

TL;DR

This paper investigates how Floquet resonances near the adiabatic limit cause non-adiabatic evolution in driven quantum systems, even with slow driving, and shows this effect persists with dissipation, making it experimentally observable.

Contribution

It reveals a general Floquet resonance phenomenon near the adiabatic limit and introduces a mapping to an extended Hilbert space to explain it, including effects of dissipation.

Findings

Resonances occur near the adiabatic limit in driven systems with quasi-degeneracies.

The phenomenon persists despite dissipation, enabling experimental observation.

A mapping to an extended Hilbert space explains the resonance behavior.

Abstract

We study the approach to the adiabatic limit in periodically driven systems. Specifically focusing on a spin-1/2 in a magnetic field we find that, when the parameters of the Hamiltonian lead to a quasi-degeneracy in the Floquet spectrum, the evolution is not adiabatic even if the frequency of the field is much smaller than the spectral gap of the Hamiltonian. We argue that this is a general phenomenon of periodically driven systems. Although an explanation based on a perturbation theory in $\omega_0$ cannot be given, because of the singularity of the zero frequency limit, we are able to describe this phenomenon by means of a mapping to an extended Hilbert space, in terms of resonances of an effective two-band Wannier-Stark ladder. Remarkably, the phenomenon survives in the presence of dissipation towards an environment and can be therefore easily experimentally observed.