High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective

Abstract

We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34}, 3379 (2000)]. We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approximation and its limitations for systems of many interacting particles.

48 pages, 7 figures

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• Effective (Floquet) Lindblad generators from spectral unwinding
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• Magnetic Order in Laser-Irradiated Kagome Antiferromagnets
• Multiple Floquet Chern insulator phases in the spin-charge coupled triangular-lattice ferrimagnet: Crucial role of higher-order terms in the high-frequency expansion
• Photo-induced Multiply Quantized Vortex States in Dirac-like Materials
• Periodically Driven Many-Body Systems: A Floquet Density Matrix Renormalization Group Study
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• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
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• Theory of Multi-photon Processes for Applications in Quantum Control
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Light-induced pseudo-magnetic fields in three-dimensional topological semimetals
• Photo-induced Non-collinear Interlayer RKKY Coupling in Bulk Rashba Semiconductors
• Floquet-Engineered Chern Insulator in two-dimensional $d_{x^2-y^2}$-Wave Altermagnets
• Artificial Gauge Field Engineered Excited-State Topology: Control of Dynamical Evolution of Localized Spinons
• Modulation of spin-orbit coupled Bose-Einstein condensates: analytical characterization of acceleration-induced transitions between energy bands
• Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Topological Phase Diagram of Optimally Shaken Honeycomb Lattices: A Dual Perspective from Stroboscopic and Non-Stroboscopic Floquet Hamiltonians
• Photoinduced Pseudospin Polarization in a Three-Orbital Hubbard Model
• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Effective dynamics and quantum state engineering by periodic kicks
• Fermi Level Fluctuations, Reduced Effective Masses and Zeeman Effect during Quantum Oscillations in Nodal Line Semimetals
• Low-frequency and Moiré Floquet engineering: a review
• Time-dependent Gutzwiller simulation of Floquet topological superconductivity
• Floquet systems with continuous dynamical symmetries: characterization, time-dependent Noether charge, and solvability
• Optical trapping of electrons in graphene
• Experimental protocol for observing single quantum many-body scars with transmon qubits
• Frequency dependence of the light-induced Hall effect in dissipative graphene
• Extended degenerate perturbation theory for the Floquet-Hilbert space
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
• Optically induced delocalization of electrons bound by attractive potentials
• Elementary excitations in the hybrid Bose-Fermi system induced by circularly polarized light in a two-dimensional gas of charge carriers with different masses
• Dynamical Confinement and Magnetic Traps for Charges and Spins
• Photo-induced directional transport in extended SSH chains
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• Optical control of electrons in a Floquet topological insulator
• Harmonic oscillator kicked by spin measurements: a Floquet-like system without classical analogous
• Floquet-Engineered Valley-Topotronics in Kekulé-Y Bond Textured Graphene Superlattice
• Dynamical stabilization by vacuum fluctuations in a cavity: Resonant electron scattering in the ultrastrong light-matter coupling regime
• Transport through Nodal Surface Semimetal-Superconductor junction in absence/presence of light irradiation
• Nonequilibrium hysteretic phase transitions in periodically light-driven superconductors
• Floquet engineering with spatially non-uniform driving fields
• Multichromatic Floquet engineering of quantum dissipation
• Study on axial fields in the dynamically assisted Schwinger effect
• Signatures of the $\pi$-mode anomaly in (1+1) dimensional periodically-driven topological/normal insulator heterostructures
• Light Control of Triplet Pairing in Correlated Electrons with Mixed-Sign Interactions
• Distinct topological excitonic insulators characterized by quantum geometry
• Many-body Keldysh Crossover in the DC-driven Haldane Spin Chain
• Onsager Reciprocal Relations for Charge and Spin Transport in Periodically Driven Systems
• $SU(N)$ spin-phonon simulations of Floquet dynamics in spin $S>1/2$ Mott insulators
• Nutation dynamics and multifrequency resonance in a many-body seesaw
• High frequency limit of spectroscopy
• Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Energy Cascade in Quantum Gases
• Topological phase transitions by time-dependent electromagnetic fields in frustrated magnets: Role of dynamical and static magnetic fields
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates
• Floquet quantum multiparameter estimation with periodic-driving-induced topological phase transition
• Dynamical Signatures of Floquet Topology in Wave Packet Dynamics
• Floquet second-order topological insulator in strained graphene
• Dirac Electrons in AC-Magnetic Fields: $\pi$-Landau Levels and Chiral Anomaly-Induced Homodyne Effect
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• Green Function Invariants for Floquet Topological Superconductivity Induced by Proximity Effects
• Characterizing the transition from topology to chaos in a kicked quantum system
• Magnetically generated spin-orbit coupling for ultracold atoms with slowly varying periodic driving
• Localization and topological signatures under periodic twisting
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems
• Anomalous radiation reaction in a circularly polarized field
• Floquet engineering of topological phases protected by emergent symmetries under resonant drives
• Robust Spin Polarization by Adiabatic Dynamical Decoupling