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Periodic driving can create topological phases of matter absent in staticsystems. In terms of the displacement of the position expectation value of atime-evolving wavepacket in a closed system, a type of adiabatic dynamics inperiodically driven systems is studied for general initial states possessingcoherence between different Floquet bands. Under one symmetry assumption, thedisplacement of the wavepacket center over one adiabatic cycle is found to becomprised by two components independent of the time scale of the adiabaticcycle: a weighted integral of the Berry curvature summed over all Floquetbands, plus an interband coherence induced correction. The found correction isbeyond a naive application of the quantum adiabatic theorem but survives in theadiabatic limit due to interband coherence. Our theoretical results are henceof general interest towards an improved understanding of the quantum adiabatictheorem. Our theory is checked using a periodically driven superlattice modelwith nontrivial topological phases. In addition to probing topological phasetransitions, the adiabatic dynamics studied in this work is now alsoanticipated to be useful in manifesting coherence and decoherence effects inthe representation of Floquet bands.

Interband Coherence Induced Correction to Adiabatic Pumping in Periodically Driven Systems