Measurement of topological invariants in a 2D photonic system

A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary(1,2). 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 bulkboundary 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(3). 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.