Effective Floquet-Gibbs states for dissipative quantum systems

Abstract

A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.

21 pages, 9 figures

References in corpus (15)

• 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
• Coherent control of dressed matter waves
• Fundamental Aspects of Quantum Brownian Motion
• Typicality for Generalized Microcanonical Ensembles
• Dissipative Floquet Topological Systems
• Coherent destruction of tunneling, dynamic localization and the Landau-Zener formula
• Condition for emergence of the Floquet-Gibbs state in periodically driven open systems
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Four-qubit device with mixed couplings
• 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
• Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models

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• Floquet engineering of molecular dynamics via infrared coupling
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• Periodically-driven Kondo impurity in nonequilibrium steady states
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• Quantum Dissipation at Conical Intersections of Quasienergies
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• The open driven two-level system at conical intersections of quasienergies
• Strong Markov dissipation in driven-dissipative quantum systems
• Enhancing the Charging Performance of Many-Body Quantum Batteries through Landau-Zener Driving
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• Floquet topological systems with flat bands: Edge modes, Berry curvature, and Orbital magnetization
• Steady state of periodically driven quantum systems