Non-dispersing wave packets in lattice Floquet systems

• URL: http://arxiv.org/abs/2005.08993v2
• Date: Wed, 17 Mar 2021 22:27:00 GMT
• Title: Non-dispersing wave packets in lattice Floquet systems
• Abstract summary: We show that non-dispersing wave packets can be realized as Floquet eigenstates. Wave packets of different $s/r$ can co-exist under the same drive, yet travel at different speeds.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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