Probing the topological Anderson transition with quantum walks

TL;DR

This paper proposes an experimental approach using quantum walks in optical networks to observe the topological Anderson transition, providing analytical predictions and simulation support for real-world implementation.

Contribution

It introduces a method to detect the topological Anderson transition via quantum walks, including analytical calculations and a practical measurement protocol.

Findings

Analytical expression for the quantum critical walk distribution

Proposed experimental protocol for observing the transition

Numerical simulations confirm feasibility with current hardware

Abstract

We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition. We analytically calculate the probability distribution describing the quantum critical walk in terms of a (time staggered) spin polarization signal and propose a concrete experimental protocol for its measurement. Numerical simulations back the realizability of our blueprint with current date experimental hardware.