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Nondispersing Wave Packets in Lattice Floquet Systems
Zhoushen Huang1, Aashish Clerk2, Ivar Martin1
1Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
Abstract:
We show that in a one-dimensional translationally invariant tight binding chain, nondispersing 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 coprime integers. Wave packets of different s/r can coexist under the same drive, yet travel at different speeds. They retain their spatial compactness either infinitely (s/r=1) or over a long time (s/r≠1). Discrete time translation symmetry is manifestly broken for s≠1, reminiscent of integer and fractional 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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