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arXiv:2003.02876 · Science Advances

General description for nonequilibrium steady states in periodically driven dissipative quantum systems

Tatsuhiko N. Ikeda, Masahiro Sato

Published Jul 3, 2020• 67 citations
arXivHTMLPDF

Abstract

Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.

DOI
10.1126/sciadv.abb4019

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Laser technology has developed and accelerated photo-induced nonequilibrium physics, from both the scientific and engineering viewpoints. Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is at the forefront of quantum physics of light-matter interaction. However, it is limited to ideal dissipationless systems. Extending Floquet engineering to various materials requires understanding of the quantum states emerging in a balance of the periodic drive and energy dissipation. Here, we derive a general description for nonequilibrium steady states (NESSs) in periodically driven dissipative systems by focusing on systems under high-frequency drive and time-independent Lindblad-type dissipation. Our formula correctly describes the time average, fluctuation, and symmetry properties of the NESS, and can be computed efficiently in numerical calculations. This approach will play fundamental roles in Floquet engineering in a broad class of dissipative quantum systems from atoms and molecules to mesoscopic systems, and condensed matter.
Nonequilibrium steady states (NESSs) in periodically driven dissipative quantum systems are vital in Floquet engineering. We develop a general theory for high-frequency drives with Lindblad-type dissipation to characterize and analyze NESSs. This theory is based on the high-frequency (HF) expansion with linear algebraic numerics and without numerically solving the time evolution. Using this theory, we show that NESSs can deviate from the Floquet-Gibbs state depending on the dissipation type. We also show the validity and usefulness of the HF-expansion approach in concrete models for a diamond nitrogen-vacancy (NV) center, a kicked open XY spin chain with topological phase transition under boundary dissipation, and the Heisenberg spin chain in a circularly-polarized magnetic field under bulk dissipation. In particular, for the isotropic Heisenberg chain, we propose the dissipation-assisted terahertz (THz) inverse Faraday effect in quantum magnets. Our theoretical framework applies to various time-periodic Lindblad equations that are currently under active research.
In this paper, we investigate periodically driven open quantum systems within the framework of Floquet-Lindblad master equations. Specifically, we discuss Lindblad master equations in the presence of a coherent, time-periodic driving and establish their general spectral features. We also clarify the notions of transient and nondecaying solutions from this spectral perspective, and then prove that any physical system described by a Floquet-Lindblad equation must have at least one physical nonequilibrium steady state (NESS), corresponding to an eigenoperator of the Floquet-Lindblad evolution superoperator UF{\mathcal{U}}_{F}UF​ with unit eigenvalue. Since the Floquet-Lindblad formalism encapsulates the entire information regarding the NESS, it in principle enables us to obtain nonlinear effects to all orders at once. The Floquet-Lindblad formalism thus provides a powerful tool for studying driven-dissipative solid-state systems, which we illustrate by deriving the nonlinear optical response of a simple two-band model of an insulating solid and comparing it with prior results established through Keldysh techniques.
Periodic driving is used to steer physical systems to unique stationary states or nonequilibrium steady states (NESS), producing enhanced properties inaccessible to nondriven systems. For open quantum systems, characterizing the NESS is challenging and existing results are generally limited to specific types of driving and the Born-Markov approximation. Here, we go beyond these limits by studying a generic periodically driven N -level quantum system interacting with a low-density thermal gas. Exploiting the framework of Floquet scattering theory, we establish general Floquet thermalization conditions constraining the nature of the NESS and the transition rates. Moreover, we examine theoretically the structure of the NESS in the high-temperature limit and find out that the NESS complies, rather surprisingly, with a uniform probability distribution (predicted by the Boltzmann law) for any driving. Numerical calculations illustrate our theoretical elaborations for a simple toy model.
This paper explores topological thermodynamics in driven dissipative quantum materials, a field at the intersection of non-equilibrium statistical mechanics, quantum topology, and condensed matter physics. We review theoretical frameworks and experimental advancements, highlighting how driving forces and dissipative processes influence the formation, stability, and characterization of topological phases. A special focus is placed on Floquet engineering for open quantum systems, where periodic driving and environmental coupling lead to novel non-equilibrium steady states with exotic topological properties. We discuss challenges in defining thermodynamic quantities like temperature and entropy in these far-from-equilibrium settings and examine how topological invariants manifest in dissipative dynamics and transport. The paper uniquely synthesizes advancements in periodically driven, open quantum systems by critically examining how dissipation, often seen as detrimental, can be precisely engineered to reveal or even stabilize topological order. This offers a distinct perspective on designing next-generation quantum technologies. Key theoretical tools, including generalized Floquet theory, Keldysh formalism, and non-Hermitian descriptions, are discussed alongside experimental platforms like photonic quantum gases and cold atomic systems.
Time-periodically driven systems are a versatile toolbox for realizing interesting effective Hamiltonians. Heating, caused by excitations to high-energy states, is a challenge for experiments. While most setups so far address the relatively weakly interacting regime, it is of general interest to study heating in strongly correlated systems. Using Floquet dynamical mean-field theory, we study nonequilibrium steady states (NESS) in the Falicov-Kimball model, with time-periodically driven kinetic energy or interaction. We systematically investigate the nonequilibrium properties of the NESS. For a driven kinetic energy, we show that resonant tunneling, where the interaction is an integer multiple of the driving frequency, plays an important role in the heating. In the strongly correlated regime, we show that this can be well understood using Fermi's golden rule and the Schrieffer-Wolff transformation for a time-periodically driven system. We furthermore demonstrate that resonant tunneling can be used to control the population of Floquet states to achieve ``photodoping.'' For driven interactions introduced by an oscillating magnetic field near a widely adopted Feshbach resonance, we find that the double occupancy is strongly modulated. Our calculations apply to shaken ultracold-atom systems and to solid-state systems in a spatially uniform but time-dependent electric field. They are also closely related to lattice modulation spectroscopy. Our calculations are helpful to understand the latest experiments on strongly correlated Floquet systems.
Quantum systems driven by a time-periodic field are a platform of condensed matter physics where effective (quasi)stationary states, termed "Floquet states", can emerge with external-field-dressed quasiparticles during driving. They appear, for example, as a prethermal intermediate state in isolated driven quantum systems or as a nonequilibrium steady state in driven open quantum systems coupled to environment. Floquet states may have various intriguing physical properties, some of which can be drastically different from those of the original undriven systems in equilibrium. In this article, we review fundamental aspects of Floquet states, and discuss recent topics and applications of Floquet states in condensed matter physics.