Long time asymptotic state of periodically driven open quantum systems

TL;DR

This paper analytically studies the long-time behavior of periodically driven open quantum systems, revealing that high-frequency driving leads to a Gibbs-like state, while finite dissipation cannot suppress excitations created by the external drive.

Contribution

It provides an analytical understanding of the asymptotic states of driven open quantum systems, highlighting the role of driving frequency and dissipation effects.

Findings

High-frequency driving results in a Gibbs distribution of a Floquet Hamiltonian.

Finite dissipation cannot suppress excitations caused by external driving.

Low-energy properties are independent of reservoir details in the high-frequency regime.

Abstract

We investigate a long time asymptotic state of periodically driven open quantum systems analytically. The model we consider in this paper is a free fermionic system coupled to an energy and particle reservoir. We clarify some generic properties of the system which are independent of the details of the reservoir in the high frequency regime of the external driving. When the frequency of the external driving is much larger than the energy cutoff of the system-reservoir coupling, the low-energy properties of the system are equivalent to those of the Gibbs distribution of a Floquet effective Hamiltonian. Furthermore, we investigate the effect of finite dissipation on the system, and elucidate that we cannot suppress excitations by merely increasing the system-reservoir coupling because the excitations are created through the reservoir by the external driving when the frequency is smaller than the energy cutoff of the system-reservoir coupling.