Measurement of topological invariants in a 2D photonic system

TL;DR

This paper demonstrates a novel experimental method to measure the topological invariant called the winding number in a 2D photonic system by observing edge spectrum shifts caused by flux insertion.

Contribution

It introduces the first measurement of the winding number in a 2D photonic system, linking edge spectrum shifts to bulk topological invariants.

Findings

Winding number measured via edge spectrum shifts

Edge spectrum resonance shifts confirm topological invariants

Method independent of microscopic details

Abstract

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk-boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number. Here, for the first time, we measure the winding number in a 2D photonic system. By inserting a unit flux quantum at the edge, we show that the edge spectrum resonances shift by the winding number. This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.