Observation of non-Hermitian topological synchronization

Non-Hermitian topology plays a pivotal role in physical science and technology, exerting a profound impact across various scientific disciplines. Recently, the interplay between topological physics and nonlinear synchronization has aroused a great interest, leading to the emergence of an intriguing phenomenon known as topological synchronization, wherein nonlinear oscillators at boundaries synchronize through topological boundary states. To the best of our knowledge, however, this phenomenon has yet to be experimentally validated, and the study of non-Hermitian topological synchronization remains in its infancy. Here, we investigate non-Hermitian topological synchronization, uncovering the influence of system size and boundary site geometry on synchronization effects. We demonstrate that simply varying the lattice size allows transitions between three distinct types of non-Hermitian topological synchronization. Furthermore, we reveal that the geometry of the boundary sites introduces a degree of freedom, enabling the control over the configuration of non-Hermitian topological synchronization. These findings are experimentally validated using non-Hermitian nonlinear topological circuits. This work significantly broadens the scope of nonlinear non-Hermitian topological physics and opens new avenues for the application of synchronization phenomena in future technologies.