Detecting topological invariants and revealing topological phase transitions in discrete-time photonic quantum walks

Abstract

We experimentally investigate topological phenomena in one-dimensional discrete-time photonic quantum walks using a combination of methods. We first detect winding numbers of the quantum walk by directly measuring the average chiral displacement, which oscillates around quantized winding numbers for finite-step quantum walks. Topological phase transitions can be identified as changes in the center of oscillation of the measured chiral displacement. The position of topological phase transition is then confirmed by measuring the moments of the walker probability distribution. Finally, we observe localized edge states at the boundary of regions with different winding numbers. We also confirm the robustness of edge states against chiral-symmetry-preserving disorder.