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.
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.
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.
In Floquet engineering, periodic driving is used to realize novel phases of matter that are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe for obtaining a static effective Hamiltonian. Although many existing works have treated closed systems, it is important to consider the effect of dissipation, which is ubiquitous in nature. Understanding the interplay of periodic driving and dissipation is a fundamental problem of nonequilibrium statistical physics that is receiving growing interest because of the fact that experimental advances have allowed us to engineer dissipation in a controllable manner. In this review, we give a detailed exposition on the formalism of quantum master equations for open Floquet systems and highlight recent work investigating whether equilibrium statistical mechanics applies to Floquet states.
The topology of quantum materials is the frontier research in condensed matter physics. In contrast with the conventional classification of materials by using the local symmetry breaking criterion, the states of quantum systems are classified according to the topology of wave functions. The potential applications of topological states may lead the traditional microelectronics to break through and accelerate the significant improvement in topological electronics. Most of the recent studies focus on the topological states of quantum systems under equilibrium conditions without external perturbations. The topological states of quantum systems far from the equilibrium under time-periodic driving have attracted wide attention. Here we first introduce the framework of Floquet engineering under the frame of the Floquet theorem. The nonequilibrium topological states of massless and massive Dirac fermions are discussed including the mechanism of phase transition. Light field driven electronic transition term in the quantum material gains extra time-dependent phase. Thereby the manipulation of effective transition term of the electron is realized to regulate the non-equilibrium topological states. We also mention how the photoinduced coherent phonon affects the nonequilibrium topological states of quantum systems from the perspective of atom manufacturing. Furthermore, research outlook on the nonequilibrium topological states is given. This review provides some clues to the design of physical properties and transport behaviors of quantum materials out of equilibrium.
Abstract We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.
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.
We theoretically investigate basic properties of nonequilibrium steady states of periodically-driven open quantum systems based on the full solution of the Maxwell–Bloch equation. In a resonant driving condition, we find that the transverse relaxation, also known as decoherence, significantly destructs the formation of Floquet states while the longitudinal relaxation does not directly affect it. Furthermore, by evaluating the quasienergy spectrum of the nonequilibrium steady states, we demonstrate that Rabi splitting can be observed as long as the decoherence time is as short as one third of the Rabi-cycle. Moreover, we find that Floquet states can be formed even under significant dissipation when the decoherence time is substantially shorter than the cycle of driving, once the driving field strength becomes strong enough. In an off-resonant condition, we demonstrate that the Floquet states can be realized even in weak field regimes because the system is not excited and the decoherence mechanism is not activated. Once the field strength becomes strong enough, the system can be excited by multi-photon absorption and the decoherence process becomes active. As a result, the Floquet states are significantly disturbed by the environment even in the off-resonant condition. Thus, we show here that the suppression of energy transfer from light to matter is a key condition for the realization of Floquet states in both on- and off-resonant conditions not only because it prevents material damage but also because it contributes to preserving coherence.