Realization of one-dimensional 2(n)-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.

Automated summary

Recently discovered square-root topological insulators are intriguing phases with inherited topological properties from the squared Hamiltonian and double-band structures. The square root mechanism has been generalized to 2(n)-root topological insulators, providing more band gaps. In this study, we experimentally realize one-dimensional 2(n)-root topological insulators in photonic waveguide arrays using the Su-Schrieffer-Heeger (SSH) model. We observe clearly visible topological edge states with tunable numbers under visible light, and demonstrate the localization and multiple numbers of edge states in 2(n)-root topological systems by visualizing the dynamic evolutions of light propagation with varying sample lengths. This experiment provides a stable platform for studying topological states with a remarkable degree of flexibility and control, by constructing 2(n)-root topological photonic lattices in various geometric arrangements.