Higher-order topological pumping and its observation in photonic lattices

TL;DR

This paper demonstrates higher-order topological pumping in photonic lattices, revealing corner-to-corner transport in 2D systems with zero dipole moments, and maps this to 3D topological insulator phenomena.

Contribution

It introduces the concept of higher-order topological pumping and experimentally observes corner transport in photonic waveguides, linking it to 3D second-order topological insulators.

Findings

Experimental verification of corner-to-corner transport in photonic lattices.

Mapping 2D topological pump to 3D hinge states.

Identification of higher-order topology in adiabatic cycles.

Abstract

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. These cycles are associated with higher-order topology and can be diagnosed by their ability to produce corner-to-corner transport in certain metamaterial platforms. We experimentally verify the corner to corner transport associated with this topological pump by using an array of photonic waveguides adiabatically modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal dimensions to three spatial dimensions, our observations are equivalent to the observation of chiral hinge states in a three-dimensional second-order topological insulator.