  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.
