A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of these edge modes is a consequence of the topological character of the bulk. For example, in an integer quantum Hall system, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The number of these edge modes, called the winding number, is a topological invariant and is related to the bulk topological invariant, the Chern number.
In this work, for the first time, we measured the winding number in a 2D photonic system. Our work was published as cover story of the March issue of Nature Photonics. We used a 2D array of coupled ring resonators, implemented on a silicon-on-insulator technology. As demonstrated earlier, by systematically positioning the rings, we can engineer a synthetic magnetic field for photons and hence implement topologically robust edge states. To measure the winding number of edge states, we introduced an additional gauge flux, coupled only to the edge, by fabricated nano-heaters on the link rings at the system boundary. These heaters change the refractive index of the ring waveguides and hence result in a gauge flux. Our experimental results demonstrate that by inserting a unit flux quantum at the edge, the edge spectrum resonances shift by their 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.
For a non-technical overview of the work, you can read this.