Floquet theorem for open systems and its applications

Abstract

For a closed system with periodic driving, Floquet theorem tells that the time evolution operator can be written as $U(t,0)\equiv P(t)e^{\frac{-i}{\hslash }{H}_{F}t}$ with $P(t+T)=P(t)$, and $H_F$ is Hermitian and time-independent called Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed systems to open systems described by a Lindblad master equation that is periodic in time. Lindbladian expansion in powers of $\frac{1}{\omega }$ is derived, where $\omega$ is the driving frequency. Two examples are presented to illustrate the theory. We find that appropriate trace preserving time-independent Lindbladian of such a periodically driven system can be constructed by the application of open system Floquet theory, and it agrees well with the exact dynamics in the high frequency limit.

5 pages, 4 figures

References in corpus (19)

• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
• The Magnus expansion and some of its applications
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Coherent control of dressed matter waves
• Single Particle Tunneling in Strongly Driven Double Well Potentials
• Exploring dynamic localization with a Bose-Einstein condensate
• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Observation of Floquet states in a strongly driven artificial atom
• Tunable spin-orbit coupling synthesized with a modulating gradient magnetic field
• Roton-Maxon Excitation Spectrum of Bose Condensates in a Shaken Optical Lattice
• Occupation of topological Floquet bands in open systems
• Unpaired Floquet Majorana fermions without magnetic fields
• Nonequilibrium Quantum Phase Transitions in the Ising Model
• Floquet systems coupled to particle reservoirs
• Expansion of matter waves in static and driven periodic potentials

Cited by in corpus (32)

• Floquet States in Open Quantum Systems
• General description for nonequilibrium steady states in periodically driven dissipative quantum systems
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• Is there a Floquet Lindbladian?
• Exact solution of time-dependent Lindblad equations with closed algebras
• Nonequilibrium steady states in the Floquet-Lindblad systems: van Vleck's high-frequency expansion approach
• Lindblad-Floquet description of finite-time quantum heat engines
• High-frequency expansions for time-periodic Lindblad generators
• Floquet exceptional contours in Lindblad dynamics with time-periodic drive and dissipation
• Floquet theory for temporal correlations and spectra in time-periodic open quantum systems: Application to squeezed parametric oscillation beyond the rotating-wave approximation
• Non-adiabatic effects in periodically driven-dissipative open quantum systems
• Floquet stroboscopic divisibility in non-Markovian dynamics
• Photon-Number-Dependent Hamiltonian Engineering for Cavities
• Breakdown of Markovianity by interactions in stroboscopic Floquet-Lindblad dynamics under high-frequency drive
• Adaptive Rotating-Wave Approximation for Driven Open Quantum Systems
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Floquet-state cooling
• Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system
• Driving-assisted open quantum transport in qubit networks
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Efficient Lindblad synthesis for noise model construction
• Dephasing-induced growth of discrete crystalline order in spin networks
• Discrete time-crystalline order in Bose-Hubbard model with dissipation
• A matrix product operator approach to non-equilibrium Floquet steady states
• Tunable quantum interference effects in Floquet two- and three-level systems
• Plateau dynamics with quantized oscillations of a strongly driven qubit
• The failure of semiclassical approach in the dissipative fully-connected Ising model
• All-optical pulse switching with a periodically driven dissipative quantum system
• Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems
• Chiral Instabilities in Driven-Dissipative Quantum Liquids
• Liouvillian topology and nonreciprocal dynamics in open Floquet chains
• Topical review on acousto-optical Floquet engineering of single-photon emitters