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.

accepted version, 22 pages, 12 figures

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Cited by in corpus (32)

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• Floquet interface states in illuminated three-dimensional topological insulators
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Effects of interactions on periodically driven dynamically localized systems
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• Layered optomagnonic structures: Time Floquet scattering-matrix approach
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• Out-of-Time-Order correlators in driven conformal field theories
• Effects of local periodic driving on transport and generation of bound states
• Realization of strongly-interacting Meissner phases in large bosonic flux ladders
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Stability of Floquet Majorana box qubits
• The Floquet Fermi Liquid
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Distributed quantum sensing with optical lattices
• Scattering-Based Characteristic Mode Theory for Structures in Arbitrary Background: Computation, Benchmarks, and Applications
• Prethermalization in aperiodically driven classical spin systems
• 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
• Charge qubits based on ultra-thin topological insulator films
• Time-resolved ARPES and optical transport properties of irradiated twisted bilayer graphene in steady-state
• Pseudospin-one particles in the time-periodic dice lattice: A new approach to transport control
• Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals
• Eikonal Approximation for Floquet Scattering