Floquet analysis of a quantum system with modulated periodic driving

Abstract

We consider a quantum system periodically driven with a strength which varies slowly on the scale of the driving period. The analysis is based on a general formulation of the Floquet theory relying on the extended Hilbert space. It is shown that the dynamics of the system can be described in terms of a slowly varying effective Floquet Hamiltonian that captures the long-term evolution, as well as rapidly oscillating micromotion operators. We obtain a systematic high-frequency expansion of all these operators. Generalizing the previous studies, the expanded effective Hamiltonian is now time-dependent and contains extra terms appearing due to changes in the periodic driving. The same applies to the micromotion operators which exhibit a slow temporal dependence in addition to the rapid oscillations. As an illustration, we consider a quantum-mechanical spin in an oscillating magnetic field with a slowly changing direction. The effective evolution of the spin is then associated with non-Abelian geometric phases reflecting the geometry of the extended Floquet space. The developed formalism is general and also applies to other periodically driven systems, such as shaken optical lattices with a time-dependent shaking strength, a situation relevant to the cold atom experiments.

arXiv commentalready published paper

References in corpus (82)

• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Experimental realisation of the topological Haldane model
• Artificial gauge potentials for neutral atoms
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Photovoltaic Hall effect in graphene
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Light-induced gauge fields for ultracold atoms
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Fractional quantum Hall states at zero magnetic field
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Spin-orbit coupling in quantum gases
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Dynamical control of matter-wave tunneling in periodic potentials
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Fractional Chern Insulator
• Superfluid-insulator transition in a periodically driven optical lattice
• Topological Flat Band Models and Fractional Chern Insulators
• Observation of the Meissner effect with ultracold atoms in bosonic ladders
• Fractional quantum Hall states of atoms in optical Lattices
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Fractional Quantum Hall Physics in Topological Flat Bands
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Irradiated graphene as a tunable Floquet topological insulator
• Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
• 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
• Coherent control of dressed matter waves
• Floquet Fractional Chern Insulator in Doped Graphene
• Effective Hamiltonians for periodically driven systems
• Spin-Orbit Coupled Quantum Gases
• Floquet engineering with quasienergy bands of periodically driven optical lattices
• Observation of photon-assisted tunneling in optical lattices
• Zoology of Fractional Chern Insulators
• Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
• Magnetically generated spin-orbit coupling for ultracold atoms
• Tunable Spin-Orbit Coupling via Strong Driving in Ultracold Atom Systems
• Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Creating artificial magnetic fields for cold atoms by photon-assisted tunneling
• Floquet Topological States in Shaking Optical Lattices
• Frustrated quantum antiferromagnetism with ultracold bosons in a triangular lattice
• Periodically-driven quantum matter: the case of resonant modulations
• Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
• Tomography of band insulators from quench dynamics
• Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
• Quantized Adiabatic Transport in Momentum Space
• Tunable spin-orbit coupling synthesized with a modulating gradient magnetic field
• Atomic spin-orbit coupling synthesized with magnetic-field-gradient pulses
• Density-Dependent Synthetic Gauge Fields Using Periodically Modulated Interactions
• Effective Hamiltonians for fastly driven many-body lattice systems
• Driven Electronic States at the Surface of a Topological Insulator
• Time Dependent Floquet Theory and Absence of an Adiabatic Limit
• Towards large-Chern-number topological phases by periodic quenching
• Floquet topological semimetal phases of an extended kicked Harper model
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Adiabatic theorem for non-hermitian time-dependent open systems
• Dynamic optical lattices of sub-wavelength spacing for ultracold atoms
• Avoided level crossing spectroscopy with dressed matter waves
• Toolbox for Abelian lattice gauge theories with synthetic matter
• The role of real-space micromotion for bosonic and fermionic Floquet fractional Chern insulators
• Effective time-independent description of optical lattices with periodic driving
• Dynamic Optical Superlattices with Topological Bands
• Kilohertz-driven Bose-Einstein condensates in optical lattices
• Shaping topological properties of the band structures in a shaken optical lattice
• Helical Floquet Channels in 1D Lattices
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Floquet systems coupled to particle reservoirs
• Comment on "Creating artificial magnetic fields for cold atoms by photon-assisted tunneling" by Kolovsky A.R
• Rice-Mele model with topological solitons in an optical lattice
• Generation of uniform synthetic magnetic fields by split driving of an optical lattice
• Tunable Chern insulator with shaken optical lattices
• Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state
• Floquet FFLO superfluids and Majorana fermions in a shaken fermionic optical lattice
• Adiabatic preparation of Floquet condensates
• Topological Floquet states on a Möbius band irradiated by circularly polarised light

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• Atomic quantum gases in periodically driven optical lattices
• Observation of anomalous π modes in photonic Floquet engineering
• Floquet dynamics in driven Fermi-Hubbard systems
• Asymptotic Prethermalization in Periodically Driven Classical Spin Chains
• Floquet Perturbation Theory: Formalism and Application to Low-Frequency Limit
• Reinforcement learning for autonomous preparation of Floquet-engineered states: Inverting the quantum Kapitza oscillator
• Parametric Instability Rates in Periodically-Driven Band Systems
• Exact Rotating Wave Approximation
• Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system
• Optically-Controlled Orbitronics on a Triangular Lattice
• Effective Floquet Hamiltonian in the low-frequency regime
• Parametric instabilities in a 2D periodically-driven bosonic system: Beyond the weakly-interacting regime
• Amplified and tunable transverse and longitudinal spin-photon coupling in hybrid circuit-QED
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Ponderomotive dynamics of waves in quasiperiodically modulated media
• Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
• Counterdiabatic Driving for Periodically Driven Systems
• Time-resolved Hall conductivity of pulse-driven topological quantum systems
• Topological Floquet engineering of a 1D optical lattice via resonantly shaking with two harmonic frequencies
• Floquet Heating in Interacting Atomic Gases with an Oscillating Force
• Generation of atypical hopping and interactions by kinetic driving
• Floquet driven frictional effects
• Floquet Spinor Bose Gases
• Floquet engineering of localized propagation of light in waveguide array
• Non-Abelian geometric phases in periodically driven systems
• How to dress radio-frequency photons with tunable momentum
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Quantum dynamics in potentials with fast spatial oscillations
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
• An SU(2) geometric phase induced by periodically driven Raman process in an ultracold dilute Bose gas
• Universal non-analytic behavior of the non-equilibrium Hall conductance in Floquet topological insulators
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator
• Transport through vertical graphene contacts under intense laser fields
• Error-Resilient Floquet Geometric Quantum Computation
• Magic running- and standing-wave optical traps for Rydberg atoms
• Floquet geometric entangling gates in ground-state manifolds of Rydberg atoms
• Switchable selective interactions in a Dicke Model with Driven Biased term
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems
• Impact of micromotion and field-axis misalignment on the excitation of Rydberg states of ions in a Paul trap
• Low-frequency and Moiré Floquet engineering: a review
• Refuting a Proposed Axiom for Defining the Exact Rotating Wave Approximation
• Magnetically generated spin-orbit coupling for ultracold atoms with slowly varying periodic driving