Floquet-Gibbs state in open quantum systems

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.

Proceedings of 14th Granada Seminar, June 20-23, 2017

References in corpus (8)

• The Magnus expansion and some of its applications
• Equilibrium states of generic quantum systems subject to periodic driving
• Periodically driven ergodic and many-body localized quantum systems
• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
• Effective Floquet-Gibbs states for dissipative quantum systems
• Dynamics of the Density Matrix in Contact with a Thermal Bath and the Quantum Master Equation
• Statistical mechanics of Floquet systems with regular and chaotic states
• Environment-governed dynamics in driven quantum systems

Cited by in corpus (8)

• Floquet States in Open Quantum Systems
• Absence of Criticality in the Phase Transitions of Open Floquet Systems
• Dynamic renormalization group theory for open Floquet systems
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Low-temperature Quantum Metrology Enhanced by Strong Couplings
• Gibbs state sampling via cluster expansions
• Frequency dependence of the light-induced Hall effect in dissipative graphene
• Out-of-time-order correlators for Swanson Hamiltonian with interaction terms