Measuring Topological Invariants in Disordered Discrete Time Quantum Walks

TL;DR

This paper demonstrates a method to measure topological invariants in disordered discrete time quantum walks using a photonic setup, revealing phase transitions and edge states under disorder.

Contribution

It implements a scattering scheme in a photonic quantum walk to directly measure topological invariants and analyze their robustness under disorder.

Findings

Successful measurement of topological invariants in quantum walks.

Observation of localized edge states at phase boundaries.

Disorder effects cause invariants to remain constant or transition continuously.

Abstract

Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally access and directly measure the topological invariants of quantum walks we implement the scattering scheme proposed by Tarasinski et al.[Phys. Rev. A 89, 042327 (2014)] in a photonic time multiplexed quantum walk experiment. The tunable coin operation provides opportunity to reach distinct topological phases, and accordingly to observe the corresponding topological phase transitions. The ability to read-out the position and the coin state distribution, complemented by explicit interferometric sign measurements, allowed the reconstruction of the scattered reflection amplitudes and thus the computation of the associated bulk topological invariants. As predicted we also find localised states at the edges between two bulks belonging to different topological phases. In order to analyse the impact of disorder we have measured invariants of two different types of disordered samples in large ensemble measurements, demonstrating their constancy in one disorder regime and a continuous transition with increasing disorder strength for the second disorder sample.