Nonlinear tuning of multiple topological edge states in photovoltaic photonic lattices.

The fusion of topology and nonlinearity has led to groundbreaking advancements in complex systems, paving the way for new discoveries and innovative device development. However, the interaction between topological states and self-defocusing nonlinearities in complex systems with multiple topological gaps has not yet been explored. Here we demonstrate two distinct topological edge solitons tuned by photovoltaic nonlinearity in Fe-doped lithium niobate waveguide arrays. By establishing a photonic nontrivial decorated Su-Schrieffer-Heeger lattice with two topological gaps, we reveal the emergence of multiple topological edge solitons derived from linear square-root edge states within these gaps. Interestingly, the bulk photovoltaic effect in Fe-doped lithium niobate crystals can generate an internal electric field that drives the electro-optical effect, enabling real-time dynamic manipulation of topological states. As a result, we experimentally observe the complete self-defocusing nonlinear tuning process of topological states within a system with multiple topological gaps, demonstrating the transitions between localization and delocalization. Our research establishes a novel platform for exploring nonlinear topology and sets the stage for further investigation into other intriguing nonlinear phenomena, offering both theoretical insights and practical applications.