Floquet-Gibbs state in open quantum systems

TL;DR

This paper investigates the conditions under which periodically driven open quantum systems reach a Floquet-Gibbs state, characterized by a thermal distribution over Floquet quasienergies, and explores the dynamics in a rotating frame.

Contribution

It introduces the Floquet-Gibbs state for open quantum systems and analyzes the conditions for its realization, including the effects of timescales and the Floquet-Magnus expansion.

Findings

Floquet-Gibbs state characterized by Boltzmann distribution over Floquet quasienergies.

Sufficient conditions for Floquet-Gibbs state depend on system-bath coupling and timescales.

Analysis of dynamics in a rotating frame provides new insights into state realization.

Abstract

We study long-time asymptotic states of periodically driven quantum systems coupled to a thermal bath. In order to describe a class of such a system, we introduce the Floquet-Gibbs state, i.e. the state whose density matrix is diagonalized in the basis of the Floquet state of the system Hamiltonian, and its diagonal element obeys the Boltzmann distribution over its Floquet quasienergy. We obtain sufficient conditions for the realization of the Floquet-Gibbs state in a system with infinitesimal system-bath coupling [T. Shirai, et al., Phys. Rev. E 91, 030101 (2015)]. These conditions severely restrict a class of suitable physical models attaining the Floquet-Gibbs state. We also show that some of the conditions can be lifted by imposing conditions on timescales of the thermal bath with the aid of the truncated Floquet Hamiltonian in the Floquet-Magnus expansion [T. Shirai, et al., New Journal of Physics 18, 053008 (2016)]. In this paper we give a overview of this theory and reconsider it by looking at the dynamics from a rotating frame.