Nonlinear signatures of Floquet band topology

TL;DR

This paper explores how nonlinear wave dynamics in Floquet lattices can be used to identify topological phases and measure Chern numbers, providing practical methods for experimental detection in photonic systems.

Contribution

It introduces novel nonlinear dynamical techniques to distinguish Floquet topological phases and measure their invariants, advancing topological photonics.

Findings

Nonlinear Bloch wave instabilities reveal Floquet band topology.

Nonlinear superposition dynamics identify symmetry inversion points.

Methods are applicable in nonlinear waveguide experiments.

Abstract

We study how the nonlinear propagation dynamics of bulk states may be used to distinguish topological phases of slowly-driven Floquet lattices. First, we show how instabilities of nonlinear Bloch waves may be used to populate Floquet bands and measure their Chern number via the emergence of nontrivial polarization textures in a similar manner to static (undriven) lattices. Second, we show how the nonlinear dynamics of non-stationary superposition states may be used to identify dynamical symmetry inversion points in the intra-cycle dynamics, thereby allowing anomalous Floquet phases to be distinguished from the trivial phase. The approaches may be readily implemented using light propagation in nonlinear waveguide arrays.