Topological synchronization of quantum van der Pol oscillators

Abstract: To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities and dissipation. This limits the applicability of this phenomenon for future devices. Here, we demonstrate a route towards significantly enhancing the robustness of synchronized behavior in open nonlinear systems that utilizes the power of topology. In a lattice of quantum van der Pol oscillators with topologically motivated couplings, boundary synchronization emerges in the classical mean field as well as the quantum model. In addition to its robustness against disorder and initial state perturbations, the observed dynamics is independent of the underlying topological insulator model provided the existence of zero-energy modes. Our work extends the notion of topology to the general nonlinear dynamics and open quantum system realm with applications to networks where specific nodes need special protection like power grids or quantum networks.