  Periodic driving can create topological phases of matter absent in static
systems. In terms of the displacement of the position expectation value of a
time-evolving wavepacket in a closed system, a type of adiabatic dynamics in
periodically driven systems is studied for general initial states possessing
coherence between different Floquet bands. Under one symmetry assumption, the
displacement of the wavepacket center over one adiabatic cycle is found to be
comprised by two components independent of the time scale of the adiabatic
cycle: a weighted integral of the Berry curvature summed over all Floquet
bands, plus an interband coherence induced correction. The found correction is
beyond a naive application of the quantum adiabatic theorem but survives in the
adiabatic limit due to interband coherence. Our theoretical results are hence
of general interest towards an improved understanding of the quantum adiabatic
theorem. Our theory is checked using a periodically driven superlattice model
with nontrivial topological phases. In addition to probing topological phase
transitions, the adiabatic dynamics studied in this work is now also
anticipated to be useful in manifesting coherence and decoherence effects in
the representation of Floquet bands.
