Non-dispersing wave packets in lattice Floquet systems

TL;DR

This paper demonstrates how to create and control non-dispersing wave packets in one-dimensional Floquet systems using inhomogeneous drives, revealing new possibilities for Floquet engineering and quantum information processing.

Contribution

It introduces a method to realize non-dispersing wave packets as Floquet eigenstates with controllable recurrence times and speeds, including drive protocols for targeted micromotion.

Findings

Wave packets can be realized as Floquet eigenstates with inhomogeneous drives.

Recurrence times lock to rational ratios of the driving period.

Different wave packets can coexist and travel at different speeds.

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 ($s/r \neq 1$). Discrete time translation symmetry is manifestly broken for $s \neq 1$, 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.