Realization of one-dimensional 2n-root topological states in photonic lattices

Square-root topological insulators recently discovered are intriguing topological phases. They possess topological properties inherited from the squared Hamiltonian and exhibit double-band structures. The mechanism of the square root was generalized to 2 n -root topological insulators, giving rise to more band gaps. In this study, we describe the experimental realization of one-dimensional 2 n -root topological insulators in photonic waveguide arrays using the archetypical Su-Schrieffer-Heeger (SSH) model. Topological edge states with tunable numbers are clearly observed under visible light. In particular, we visualized the dynamic evolutions of the light propagation by varying the sample lengths, which further proved the localization and multiple numbers of edge states in 2 n -root topological systems. The experiment, which involves constructing 2 n -root topological photonic lattices in various geometric arrangements, provides a stable platform for studying topological states that exhibit a remarkable degree of flexibility and control.