Non-dispersing wave packets in lattice Floquet systems
Abstract
We show that in a one-dimensional translationally invariant tight binding chain, non-dispersing wave packets can in general be realized as Floquet eigenstates -- or linear combinations thereof -- using a spatially inhomogeneous drive, which can be as simple as modulation on a single site. The recurrence time of these wave packets (their "round trip" time) locks in at rational ratios sT/r of the driving period T, where s,r are co-prime integers. Wave packets of different s/r can co-exist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r=1) or over long time (s/r ≠ 1). Discrete time translation symmetry is manifestly broken for s ≠ 1, reminiscent of Floquet time crystals. We further demonstrate how to reverse-engineer a drive protocol to reproduce a target Floquet micromotion, such as the free propagation of a wave packet, as if coming from a strictly linear energy spectrum. The variety of control schemes open up a new avenue for Floquet engineering in quantum information sciences.