Floquet dynamics under spatially inhomogeneous drive

Floquet engineering has been shown to be a promising mechanism in realizing quantum information manipulations. While spatially homogeneous drives allow for block diagonalization in momentum, and have thus often been invoked in theoretical studies, in realistic systems, translation symmetry is typically broken. In this work, we discuss features of Floquet systems under inhomogeneous spatial drives, in the context of band theory, such as nondispersing traveling wave packets, simplification of dynamical Hilbert space, and a machine learning scheme which can predict time dynamics of arbitrary temporal driving profiles.