Simulating Floquet non-Abelian topological insulator with photonic quantum walks

TL;DR

This paper demonstrates the first experimental simulation and characterization of Floquet non-Abelian topological insulators using photonic quantum walks, revealing their unique bulk-boundary correspondence and non-Abelian topological features.

Contribution

It introduces a novel photonic quantum walk approach to simulate FNATIs and develops dynamic measurement schemes to observe their key topological signatures.

Findings

Successful simulation of FNATI using photonic quantum walks

Experimental detection of non-Abelian topological charges

Observation of multifold bulk-boundary correspondence

Abstract

Floquet non-Abelian topological phases emerge in periodically driven systems and exhibit properties that are absent in their Abelian or static counterparts. Dubbed the Floquet non-Abelian topological insulators (FNATIs), they are characterized by non-Abelian topological charges and feature multifold bulk-boundary correspondence, making their experimental observation challenging. Here we simulate the FNATI using a higher-dimensional photonic quantum walk and develop dynamic measurement schemes to demonstrate key signatures of the FNATI. Importantly, combining a direct bulk-dynamic detection for the underlying quaternion topological charge, and a spatially-resolved injection spectroscopy for the edge states, we experimentally establish the multifold bulk-boundary correspondence, and, in particular, identify the anomalous non-Abelian phase where edge states appear in all band gaps, despite the presence of a trivial topological charge. Our experiment marks the first experimental characterization of the FNATI, providing general insight into the non-Abelian topological phases.