Photonic non-Abelian topological insulators with six bands

Non-Abelian topological insulators are multi-band systems, satisfying parity-time symmetry, characterized by fully gapped bands and whose topological charges are non-Abelian quaternions. These systems provide a richer landscape of edge and domain-wall states compared to that predicted by the Zak phase framework for Abelian topological insulators. Although non-Abelian topological insulators have been demonstrated in some proof-of-concept platforms, their realization in a photonic platform, where their characteristics are particularly valuable for on-chip applications, remains out of reach due to the lack of a feasible model. Here, we propose a minimal model for non-Abelian topological insulators and experimentally realize a six-band system at optical frequencies by using photonic waveguide arrays. A number of non-Abelian topological charges is experimentally demonstrated by probing the adiabatic evolution of edge states in a system with varying structural parameters. At the boundary between two samples with different non-Abelian topological charges, we experimentally observe domain-wall states that adhere to a non-Abelian quotient relation. The proposed idea can be generalized to an arbitrary number of bands and offers the flexibility to control multiple edge and domain-wall states in photonic devices.