Quantized frequency-domain polarization of driven phases of matter

Abstract

Periodically driven quantum systems can realize novel phases of matter that do not exist in static settings. We study signatures of these drive-induced phases on the $(d+1)$-dimensional Floquet lattice, comprised of $d$ spatial dimensions plus the frequency domain. The average position of Floquet eigenstates along the frequency axis can be written in terms of a non-adiabatic Berry phase, which we interpret as frequency-domain polarization. We argue that whenever this polarization is quantized to a nontrivial value, the phase of matter cannot be continuously connected to a time-independent state and, as a consequence, it captures robust properties of its dynamics. We illustrate this in driven topological phases, such as superconducting wires and the anomalous Floquet Anderson insulator; as well as in driven symmetry-broken phases, such as time crystals. We further introduce a new dynamical phase of matter that we construct by imposing quantization conditions on its frequency-domain polarization. This illustrates the potential for using this kind of polarization as a tool to search for new driven phases of matter.