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 (9)

• Periodically-driven quantum matter: the case of resonant modulations
• Interaction dependent heating and atom loss in a periodically driven optical lattice
• Floquet interface states in illuminated three-dimensional topological insulators
• Population dynamics in Floquet realisation of Harper-Hofstadter Hamiltonian
• Effects of interactions on periodically driven dynamically localized systems
• Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
• Layered optomagnonic structures: Time Floquet scattering-matrix approach
• Effects of local periodic driving on transport and generation of bound states
• Parametric Instabilities in Resonantly-Driven Bose-Einstein Condensates