Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

TL;DR

This paper introduces a method to detect topological invariants, specifically Zak phases, in one-dimensional chiral quantum systems using photonic quantum walks, validated through experiments and robustness tests.

Contribution

It proposes and experimentally validates a universal method to measure bulk topological properties in 1D chiral systems via mean chiral displacement.

Findings

Successfully measured Zak phases in photonic quantum walks.

Demonstrated robustness of the detection method against dynamical disorder.

Characterized the full phase diagram of a Floquet system.

Abstract

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.