Non-Abelian Topological Phase Transition under Duality Symmetry Mapping in a One-Dimensional Photonic System

Dualities, regarded as hidden symmetries, map seemingly unrelated physical systems onto each other, which share identical energy spectra and dynamic characteristics. However, to date, there has been scant research investigating the non-Abelian topological phases and topological phase transition between two dual parts. Here, exploiting the coupling of two degenerate polarized defected modes in one-dimensional photonic crystals with uniaxial crystals, we reveal a non-Abelian topological phase transition of two systems associated with duality symmetry. We demonstrate that two dual systems share identical Abelian invariants (that is, Zak phase and winding number) but could be in different non-Abelian topological phases, described by generalized quaternion group Q16. The self-dual point is exactly the non-Abelian topological phase transition point. The robust topological edge states can be theoretically predicted by the combination of non-Abelian topological charges and winding number and further numerically verified. Our work presents rich non-Abelian topological phase transitions in a simple photonic system with hidden duality symmetry, paving the way for further non-Abelian topological research and topological photonic applications.