Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields

Abstract

Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter systems. Here, we develop a general formalism that captures the essential features ruling the dynamics: the effective Hamiltonian, but also the effects related to the initial phase of the modulation and the micro-motion. This framework allows for the identification of driving schemes, based on general N-step modulations, which lead to configurations relevant for quantum simulation. In particular, we explore methods to generate synthetic spin-orbit couplings and magnetic fields in cold-atom setups.

25 pages, 6 figures, includes Appendices (A-K). An erroneous factor of two has been corrected in the last term of Eq. C10 (Appendix C); this typo had no impact on the rest of the article

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• Fractional quantum Hall states of atoms in optical Lattices
• Artificial graphene as a tunable Dirac material
• Floquet-Bloch theory and topology in periodically driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Floquet chiral edge states in graphene
• Gauge fields for ultracold atoms in optical superlattices
• Floquet Fractional Chern Insulator in Doped Graphene
• Tuning laser-induced bandgaps in graphene
• Effective Hamiltonians for periodically driven systems
• Floquet generation of Majorana end modes and topological invariants
• Spin-Orbit Coupled Quantum Gases
• Many-body energy localization transition in periodically driven systems
• Non-Abelian gauge potentials in graphene bilayers
• Periodic thermodynamics of isolated systems
• Exploring dynamic localization with a Bose-Einstein condensate
• Merging of Dirac points and Floquet topological transitions in AC driven graphene
• Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
• Magnetically generated spin-orbit coupling for ultracold atoms
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
• Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
• Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice
• Synthetic Gauge Fields for Vibrational Excitations of Trapped ions
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• Radiation effects on the electronic structure of bilayer graphene
• Analog of photon-assisted tunneling in a Bose-Einstein condensate
• Efficient computation of the Zassenhaus formula
• Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
• Interferometric approach to measuring band topology in 2D optical lattices
• Atomic spin-orbit coupling synthesized with magnetic-field-gradient pulses
• Chiral Rashba spin textures in ultra-cold Fermi gases
• Time Averaged Quantum Dynamics and the Validity of the Effective Hamiltonian Model
• Counter-propagating edge modes and topological phases of a kicked quantum Hall system
• Ultracold Lattice Gases with Periodically Modulated Interactions
• Dirac Cones, Topological Edge States, and Nontrivial Flat Bands in Two-Dimensional Semiconductors with a Honeycomb Nanogeometry
• Spin-orbit coupling in a graphene bilayer and in graphite
• Engineering Quantum Anomalous Hall Plateaus and Anti-Chiral States with AC Fields
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Quantum simulation of correlated-hopping models with fermions in optical lattices
• Periodically-driven cold atoms: the role of the phase
• AC-induced superfluidity
• Effective time-independent description of optical lattices with periodic driving
• Dynamic Optical Superlattices with Topological Bands
• Energy flow in periodic thermodynamics
• Photon-Assisted-Tunneling Toolbox for Quantum Simulations in Ion Traps
• Topological Superfluid Transition Induced by Periodically Driven Optical Lattice
• Directed transport in driven optical lattices by phase generation
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• Bosonic Topological Excitations from the Instability of a Quadratic Band Crossing
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• Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system
• Chiral current in Floquet cavity-magnonics
• Inverted many-body mobility edge in a central qudit problem
• Generalized cold-atom simulators for vacuum decay
• Floquet topological phases with large winding number
• Quasiparticles of periodically driven quantum dot coupled between superconducting and normal leads
• Floquet-Band Engineering of Shaken Bosonic Condensates
• Non-Abelian geometric phases in periodically driven systems
• Steady-state superconductivity in electronic materials with repulsive interactions
• High-Frequency Analysis of Effective Interactions and Bandwidth for Transient States after Monocycle Pulse Excitation of Extended Hubbard Model
• Dynamical Generation of Topological Magnetic Lattices for Ultracold Atoms
• Robust effective ground state in a nonintegrable Floquet quantum circuit
• Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: monodromy matrix approach
• Fano resonances in optical spectra of semiconductor quantum wells driven by an oscillating field
• Strong Disorder Renormalization for the dynamics of Many-Body-Localized systems : iterative elimination of the fastest degree of freedom via the Floquet expansion
• Divergence of the Floquet-Magnus expansion in a periodically driven one-body system with energy localization
• Floquet engineering of many-body states by the ponderomotive potential
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Quantum metrology with precision reaching beyond-$1/N$ scaling through $N$-probe entanglement generating interactions
• Two-flux tunable Aharonov-Bohm caging in a photonic lattice
• Anomalous levitation and annihilation in Floquet topological insulators
• Universal long-time behavior of stochastically driven interacting quantum systems
• Spin-imbalance-induced transverse magnetization in the Hofstadter-Hubbard model
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands
• Simulating systems of itinerant spin-carrying particles using arrays of superconducting qubits and resonators
• Floquet engineering of molecular dynamics via infrared coupling
• A cavity-microscope for micrometer-scale control of atom-photon interactions
• Light-induced Odd-parity Magnetism in Conventional Collinear Antiferromagnets
• How to dress radio-frequency photons with tunable momentum
• Dynamical localization in non-Hermitian quasi-crystals
• Light-induced odd-parity altermagnets on dimerized lattices
• Anomalous Floquet Phases. A resonance phenomena
• Accelerated creation of NOON states with ultracold atoms via counterdiabatic driving
• Interplay of Floquet Lifshitz transitions and topological transitions in bilayer Dirac materials
• Many-body nonequilibrium dynamics in a self-induced Floquet system
• Dynamical chaotic phases and constrained quantum dynamics
• Nonlinear spectroscopy of high-spin fluctuations
• Observation of Chiral-Mode Domains in a Frustrated XY Model on Optical Triangular Lattices
• Effective Hamiltonian with tunable mixed pairing in driven optical lattices
• Tuning of Bilayer Graphene Heterostructure by Horizontally Incident Circular Polarized Light
• Sharp detection of the onset of Floquet heating using eigenstate sensitivity
• Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors
• Non-perturbative Floquet engineering of the toric-code Hamiltonian and its ground state
• Floquet engineering triplet superconductivity in superconductors with spin-orbit coupling or altermagnetism
• Photo-induced SU(3) topological material of spinless fermions
• Dynamic renormalization group theory for open Floquet systems
• Single atom edge-like states via quantum interference
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Universal Counterdiabatic Driving
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Real-time dynamics of the photoinduced topological state in organic conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under continuous-wave and pulse excitations
• Floquet engineering flat bands for bosonic fractional quantum Hall in small lattices
• Topological phonons in arrays of ultracold dipolar particles
• Fractional topological insulator precursors in spin-orbit fermion ladders
• Floquet States
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Quantum dynamics in potentials with fast spatial oscillations
• Phase transition in a Aubry-Andre system with rapidly oscillating magnetic field
• Floquet Hamiltonian Engineering of an Isolated Many-Body Spin System
• Topological Insulators with Hybrid-order Boundary States
• Multimode N00N states in driven atomtronic circuits
• Chiral Luttinger liquids in graphene tuned by irradiation
• Fluctuations of the order parameter of a mesoscopic Floquet condensate
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Artificial magnetic field for synthetic quantum matter without dynamical modulation
• Floquet engineering of the Lifshitz phase transition in the Hubbard model
• Intertwined Space-Time Symmetry, Orbital Magnetism and Dynamical Berry Curvature in a Circularly Shaken Optical Lattice
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• A Multi-Purpose Platform for Analog Quantum Simulation
• Meissner effect in Fock space
• Nonequilibrium dynamics of spin-orbit coupled lattice bosons
• Floquet Engineering of Lie Algebraic Quantum Systems
• Driven Bose-Hubbard Model with a Parametrically Modulated Harmonic Trap
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Harmonic dual dressing of spin one-half systems
• Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields
• Universal non-analytic behavior of the non-equilibrium Hall conductance in Floquet topological insulators
• Particle production and hadronization temperature in the massive Schwinger model
• Anyonic phase transitions in the 1D extended Hubbard model with fractional statistics
• Nonlinear signatures of Floquet band topology
• Floquet Spin Splitting and Spin Generation in Antiferromagnets
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Dynamical Quantum Phase Transitions in presence of a spin bath
• Density dependent gauge field inducing emergent SSH physics, solitons and condensates in a discrete nonlinear Schrödinger equation
• Floquet analysis of extended Rabi models based on high-frequency expansion
• Full tunability and quantum coherent dynamics of a driven multilevel system
• Optical Conductivity Signatures of Floquet Electronic Phases
• Laser induced surface magnetization in Floquet-Weyl semimetals
• Error-Resilient Floquet Geometric Quantum Computation
• Individually tunable tunnelling coefficients in optical lattices using local periodic driving
• Universal quantum processors in spin systems via robust local pulse sequences
• Transport on a topological insulator surface with a time-dependent magnetic barrier
• Floquet Flux Attachment in Cold Atomic Systems
• Floquet expansion by counting pump photons
• Extended unitarity and absence of skin effect in periodically driven systems
• Single and multi-frequency driving protocols in a Rashba nanowire proximitized to an s-wave superconductor
• Dynamical instability towards finite-momentum pairing in quenched BCS superconducting phases
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Quantum Optimization on Rydberg Atom Arrays with Arbitrary Connectivity: Gadgets Limitations and a Heuristic Approach
• Driven Topological Systems in the Classical Limit
• Directed motion of doublons and holes in periodically driven Mott insulators
• Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
• Controllable Floquet edge modes in a multi-frequency driving system
• Wave manipulation via delay-engineered periodic potentials
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Manipulating Cooper pairs with a controllable momentum in periodically driven degenerate Fermi gases
• Floquet theory and applications in open quantum and classical systems
• Floquet-driven crossover from density-assisted tunneling to enhanced pair tunneling
• Determination of Chern numbers with a phase retrieval algorithm
• Correspondence between a shaken honeycomb lattice and the Haldane model
• The Future of the Correlated Electron Problem
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
• Structure-dynamics relation in shaken optical lattices
• Inducing anisotropies in Dirac fermions by periodic driving
• Two-leg fermionic Hubbard ladder system in the presence of state-dependent hopping
• Fulde-Ferrell superfluids in spinless ultracold Fermi gases
• Site-selective particle deposition in periodically driven quantum lattices
• Modulation-induced long-range magnon bound states in one-dimensional optical lattices
• Steering spin fluctuations in lattice systems via two-tone Floquet engineering
• Continuously tracked, stable, large excursion trajectories of dipolar coupled nuclear spins
• Floquet defect solitons
• Understanding Floquet Resonances in Ultracold Gas Scattering
• Topological Chiral Edge States in a Synthetic Dimension of Atomic Trap States
• Optically Induced Topological Phase Transition in two dimensional Square Lattice Antiferromagnet
• Quantum transport phenomena induced by time-dependent fields
• Dynamics of weakly interacting bosons in optical lattices with flux
• Scale Invariance in the Lowest Landau Level
• Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials
• All-optical control of excitons in semiconductor quantum wells
• Dynamical freezing and switching in periodically driven bilayer graphene
• Encoding position by spins: Objectivity in the boson-spin model
• Simulation of chiral motion of excitation within the ground-state manifolds of neutral atoms
• Error bounds for the Floquet-Magnus expansion and their application to the semiclassical quantum Rabi model
• Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids
• Floquet analysis of time-averaged trapping potentials
• Autonomous Stabilization of Floquet States Using Static Dissipation
• Design algorithms of driving-induced nonreciprocal components
• Dynamical preparation of an atomic condensate in a Hofstadter band
• Characterizing Floquet topological phases by quench dynamics: A multiple-subsystem approach
• Orbital Inverse Faraday and Cotton-Mouton Effects in Hall Fluids
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Stable Collective Dynamics of Two-Level Systems Coupled by Dipole Interactions
• Chiral excitation flows of a multinode network based on synthetic gauge fields
• Floquet prethermalization with lifetime exceeding 90s in a bulk hyperpolarized solid
• Oscillating Fields, Emergent Gravity and Particle Traps
• Valley Gapless Semiconductor: Models and Applications
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Self-energy functional theory with symmetry breaking for disordered lattice bosons
• Photoinduced dc Hall current in few-layer black phosphorus with a gate-tunable Floquet gap
• Supersymmetry dynamics on Rydberg atom arrays
• Walsh-Floquet Theory of Periodic Kick Drives
• Theory of quasiparticle generation by microwave drives in superconducting qubits
• Floquet dynamical chiral spin liquid at finite frequency
• Proposal for realizing quantum-spin systems on a two-dimensional square lattice with Dzyaloshinskii-Moriya interaction by Floquet engineering using Rydberg atoms
• Spin-dependent Andreev reflection in spin-orbit coupled systems by breaking time-reversal symmetry
• Singularities of Floquet Scattering and Tunneling
• Floquet-Engineering Weyl Points and Linked Fermi Arcs from Straight Nodal Lines
• Developing a semiclassical Wentzel-Kramers-Brillouin theory for $\alpha -{\mathcal{T}}_3$ model
• Control over few photon pulses by a time-periodic modulation of the photon-emitter coupling
• Computing Floquet quasienergies in finite and extended systems: Role of electromagnetic and quantum-geometric gauges
• Quantum control without quantum states
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Multiple Floquet Chern insulator phases in the spin-charge coupled triangular-lattice ferrimagnet: Crucial role of higher-order terms in the high-frequency expansion
• Electronic states bound by repulsive potentials in graphene irradiated by a circularly polarized electromagnetic field
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems
• Stability of superfluids in tilted optical lattices with periodic driving
• On the different Floquet Hamiltonians in a periodic-driven Bose-Josephson junction
• Topological Phase Transitions with Zero Indirect Band Gap
• Simulation of nodal-line semimetal in amplitude-shaken optical lattices
• Strong frequency dependence of transport in the driven Fano-Anderson model
• Many topological regions on the Bloch sphere of the spin-1/2 double kicked top
• Magnetic Order in Laser-Irradiated Kagome Antiferromagnets
• Generating topological optical flux lattices for ultracold atoms by modulated Raman and radio-frequency couplings
• Topological Phase Diagram of Optimally Shaken Honeycomb Lattices: A Dual Perspective from Stroboscopic and Non-Stroboscopic Floquet Hamiltonians
• Multipassage Landau-Zener tunneling oscillations in transverse/longitudinal dual dressing of atomic qubits
• Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations
• Two-particle topological Thouless spin pump
• Dissipation and non-thermal states in cryogenic cavities
• Floquet vacuum engineering: Laser-driven chiral soliton lattice in the QCD vacuum
• Resonant dynamics of dipole-conserving Bose-Hubbard model with time-dependent tensor electric fields
• Localized Floquet states in gated bilayer graphene induced by a focused optical beam with orbital angular momentum
• Generating scalable entanglement of ultracold bosons in superlattices through resonant shaking
• Topological Phase Transitions and Edge-State Transfer in Time-Multiplexed Quantum Walks
• Extended Haldane model -- a modern gateway to topological insulators
• Experimental protocol for observing single quantum many-body scars with transmon qubits
• Floquet Schrieffer-Wolff transform based on Sylvester equations
• Thermometry of Trapped Ions Based on Bichromatic Driving
• Degree of simplicity of Floquet states of a periodically driven Bose-Hubbard dimer
• Resonant dynamics of spin cluster in a periodically driven one-dimensional Rydberg lattice
• Fourier Neural Operators for Time-Periodic Quantum Systems: Learning Floquet Hamiltonians, Observable Dynamics, and Operator Growth
• Photoinduced Pseudospin Polarization in a Three-Orbital Hubbard Model
• Reciprocal Floquet thermalization in one-dimensional Rydberg atom array
• Theory of Multi-photon Processes for Applications in Quantum Control
• Instability and particle current control of a parametrically driven Bose-Einstein condensate in a ring-shaped lattice
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Effective dynamics and quantum state engineering by periodic kicks
• Sachdev-Ye-Kitaev physics from the Hubbard model: A Floquet engineering approach
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Quantum simulation of fermionic non-Abelian lattice gauge theories in $(2+1)$D with built-in gauge protection
• Photon-mediated electronic correlation effects in irradiated two-dimensional Dirac systems
• The mixing-spacetime symmetry in the Floquet-Bloch band theory
• Multichromatic Floquet engineering of quantum dissipation
• Localization Dynamics from Static and Mobile Impurities
• Study on axial fields in the dynamically assisted Schwinger effect
• A theorem regarding families of topologically non-trivial fermionic systems
• Topological anomalous Floquet photon pump
• Unpolarized prethermal discrete time crystal
• Generalized pulse design in Floquet engineering: Application to interacting spin systems
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene
• Characterizing the transition from topology to chaos in a kicked quantum system
• Suppression of scattering from slow to fast subsystems and application to resonantly Floquet-driven impurities in strongly interacting systems
• Topological two-particle dynamics in a periodically driven lattice model with on-site interactions
• Noise resilience of two-dimensional Floquet topological phases
• Control of memory effects in a spin-boson system by periodic driving
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain
• Phase diagrams of spin-2 Floquet spinor Bose-Einstein condensates
• Extended degenerate perturbation theory for the Floquet-Hilbert space
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal
• Detuning the Floquet anomalous chiral spin liquid
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• Topological energy pumping in a quasi-periodically driven four-level system
• Magnetically generated spin-orbit coupling for ultracold atoms with slowly varying periodic driving
• Optical creation of dark-bright soliton lattices in one-dimensional multicomponent Bose-Einstein condensates
• Fractionalized Prethermalization in the One-Dimensional Hubbard Model
• Detecting degenerate bands topological invariants in optical lattice
• Floquet quantum multiparameter estimation with periodic-driving-induced topological phase transition
• Dynamical Signatures of Floquet Topology in Wave Packet Dynamics
• Emergence of caustics in dynamics of the Kitaev model
• Quantum spin liquids bootstrapped from Ising criticality in Rydberg arrays
• Nutation dynamics and multifrequency resonance in a many-body seesaw
• Dynamical Confinement and Magnetic Traps for Charges and Spins
• 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 stabilization by vacuum fluctuations in a cavity: Resonant electron scattering in the ultrastrong light-matter coupling regime
• Field-induced topological pair-density wave states in a multilayer optical lattice
• Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving
• Geometrical frustration, power law tunneling and non-local gauge fields from scattered light
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems
• Effective Hamiltonians for almost-periodically driven quantum systems
• Distinct topological excitonic insulators characterized by quantum geometry
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
• Floquet engineering with spatially non-uniform driving fields
• Long term behavior of the stirred vacuum on a Dirac chain: geometry blur and the random Slater ensemble
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice
• Multimode NOON-state generation with ultracold atoms via geodesic counterdiabatic driving
• Anomalous radiation reaction in a circularly polarized field