Scattering Theory for Floquet-Bloch States

Abstract

Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasi-energy, which is defined only up to the addition of integer multiples of $\hslash \omega$ for a Hamiltonian with period $T=2\pi /\omega$. We discuss the consequences of this for the interpretation of "elastic" and "inelastic" scattering in cases of physical interest. We illustrate our general results with applications to: the scattering of a single particle in a Floquet-Bloch state from a static potential; and, the scattering of two particles in Floquet-Bloch states through their interparticle interaction. We analyse examples of these scattering processes that are closely related to the schemes used to general artifical gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit $\omega \to \infty$ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stablize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in current experimental set-up can be switched off by additional confinement of transverse motion.

arXiv commentaccepted version, 22 pages, 12 figures

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Cited by in corpus (90)

• Atomic quantum gases in periodically driven optical lattices
• Topological Bands for Ultracold Atoms
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• Topological singularities and the general classification of Floquet-Bloch systems
• Amplified Emission by Atoms and Lasing in Photonic Time Crystals
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Artificial gauge fields in materials and engineered systems
• Tailoring quantum gases by Floquet engineering
• Observation of Bose-Einstein Condensation in a Strong Synthetic Magnetic Field
• Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths
• Periodically-driven quantum matter: the case of resonant modulations
• Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
• Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap
• Heating and many-body resonances in a periodically driven two-band system
• Interaction dependent heating and atom loss in a periodically driven optical lattice
• Creating State-Dependent Lattices for Ultracold Fermions by Magnetic Gradient Modulation
• Towards large-Chern-number topological phases by periodic quenching
• Multiphoton interband excitations of quantum gases in driven optical lattices
• Floquet dynamics in driven Fermi-Hubbard systems
• The Floquet-Boltzmann equation
• Asymptotic Prethermalization in Periodically Driven Classical Spin Chains
• Floquet interface states in illuminated three-dimensional topological insulators
• Reinforcement learning for autonomous preparation of Floquet-engineered states: Inverting the quantum Kapitza oscillator
• Dynamic optical lattices of sub-wavelength spacing for ultracold atoms
• Random multipolar driving: tunably slow heating through spectral engineering
• Parametric Instability Rates in Periodically-Driven Band Systems
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Effects of interactions on periodically driven dynamically localized systems
• Mobility edge and multifractality in a periodically driven Aubry-André model
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• Parametric instabilities of interacting bosons in periodically-driven 1D optical lattices
• Universal chiral quasi-steady states in periodically driven many-body systems
• Time-induced second-order topological superconductors
• Steady state of interacting Floquet insulators
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• Layered optomagnonic structures: Time Floquet scattering-matrix approach
• Interband heating processes in a periodically driven optical lattice
• Effective Long-distance Interaction from Short-distance Interaction in Periodically Driven One-dimensional Classical System
• The Floquet Engineer's Handbook
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Spin-momentum coupled Bose-Einstein condensates with lattice band pseudospins
• The optimal frequency window for Floquet engineering in optical lattices
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Nonequilibrium Steady States and Resonant Tunneling in Time-Periodically Driven Systems with Interactions
• Out-of-Time-Order correlators in driven conformal field theories
• Conformal Floquet dynamics with a continuous drive protocol
• Effects of local periodic driving on transport and generation of bound states
• Floquet bound states around defects and adatoms in graphene
• Realization of strongly-interacting Meissner phases in large bosonic flux ladders
• Floquet-Drude conductivity
• Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Anomalous Floquet tunneling in uniaxially strained graphene
• Ab-initio Theory of Photoionization via Resonances
• The Floquet Fermi Liquid
• Stability of Floquet Majorana box qubits
• Resonant excitations of a Bose Einstein condensate in an optical lattice
• Stability of a Bose-Einstein condensate in a driven optical lattice: Crossover between weak and tight transverse confinement
• Floquet Heating in Interacting Atomic Gases with an Oscillating Force
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Dynamics of fluctuation correlation in periodically driven classical system
• Distributed quantum sensing with optical lattices
• Scattering and perturbation theory for discrete-time dynamics
• Self-adapted Floquet Dynamics of Ultracold Bosons in a Cavity
• Floquet scattering of light and sound in Dirac optomechanics
• Two- and three-body problem with Floquet-driven zero-range interactions
• Floquet-Band Engineering of Shaken Bosonic Condensates
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Direct cooling in an optical lattice by amplitude modulation
• Prethermalization in aperiodically driven classical spin systems
• Scattering-Based Characteristic Mode Theory for Structures in Arbitrary Background: Computation, Benchmarks, and Applications
• Stabilization of prethermal Floquet steady states in a periodically driven dissipative Bose-Hubbard model
• Floquet theory for the electronic stopping of projectiles in solids
• Discrete Time Crystal Phase of Higher Dimensional Integrable Models
• Theory of quasiparticle generation by microwave drives in superconducting qubits
• Stability of superfluids in tilted optical lattices with periodic driving
• Quasi-one-dimensional Hall physics in the Harper-Hofstadter-Mott model
• Control over few photon pulses by a time-periodic modulation of the photon-emitter coupling
• Charge qubits based on ultra-thin topological insulator films
• Time-resolved ARPES and optical transport properties of irradiated twisted bilayer graphene in steady-state
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals
• Time-dependent transport through a T-coupled quantum dot
• Pseudospin-one particles in the time-periodic dice lattice: A new approach to transport control
• Eikonal Approximation for Floquet Scattering
• Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates