Scattering theory for FloquetBloch 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 timeperiodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the singleparticle dynamics can be described in terms of spatially extended FloquetBloch waves. We develop a general formalism for the scattering of these FloquetBloch waves. An important role is played by the conservation of Floquet quasienergy, which is defined only up to the addition of integer multiples of ℏ ω for a Hamiltonian with period T =2 π /ω . 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 FloquetBloch state from a static potential and the scattering of two bosonic particles in FloquetBloch states through their interparticle interaction. We analyze examples of these scattering processes that are closely related to the schemes used to generate artificial gauge fields in coldatom experiments, through optical dressing of internal states, or through timeperiodic modulations of tightbinding lattices. We show that the effects of scattering cannot, in general, be understood by an effective timeindependent Hamiltonian, even in the limit ω →∞ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stabilize manybody phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in the current experimental setup can be switched off by additional confinement of transverse motion.
 Publication:

Physical Review A
 Pub Date:
 March 2015
 DOI:
 10.1103/PhysRevA.91.033601
 arXiv:
 arXiv:1410.5364
 Bibcode:
 2015PhRvA..91c3601B
 Keywords:

 67.85.Hj;
 03.75.b;
 BoseEinstein condensates in optical potentials;
 Matter waves;
 Condensed Matter  Quantum Gases
 EPrint:
 accepted version, 22 pages, 12 figures