Simulating Floquet non-Abelian topological insulator with photonic quantum walks

• URL: http://arxiv.org/abs/2508.06466v1
• Date: Fri, 08 Aug 2025 17:14:50 GMT
• Title: Simulating Floquet non-Abelian topological insulator with photonic quantum walks
• Authors: Quan Lin, Tianyu Li, Haiping Hu, Wei Yi, Peng Xue,
• Abstract summary: Floquet non-Abelian topological insulators are characterized by non-Abelian topological charges and feature multifold bulk-boundary correspondence.<n>We simulate the FNATI using a higher-dimensional photonic quantum walk and develop dynamic measurement schemes to demonstrate key signatures.<n>Our experiment marks the first experimental characterization of the FNATI, providing general insight into the non-Abelian topological phases.
• Score: 7.581952650801906
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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