  Higher order topological insulators (HOTI) have emerged as a new class of
phases, whose robust in-gap "corner" modes arise from the bulk higher-order
multipoles beyond the dipoles in conventional topological insulators. Here, we
incorporate Floquet driving into HOTI's, and report for the first time a
dynamical polarization theory with anomalous non-equilibrium multipoles.
Further, a proposal to detect not only corner states but also their dynamical
origin in cold atoms is demonstrated, with the latter one never achieved
before. Experimental determination of anomalous Floquet corner modes are also
proposed.
