Nonlinear Thouless pumping of solitons across an impurity

The nonlinear Thouless pumping is an exciting frontier of topological physics. While recent works have revealed the quantized motion of solitons in Thouless pumps, the interplay between the topology, nonlinearity, and disorder remains largely unexplored. Here, we investigate the nonlinear Thouless pumping of solitons in the presence of an impurity in the context of a Bose–Einstein condensate. Using both the Gross-Pitaevskii equation and Lagrange variational approach, we analyze the interaction between a moving soliton and an impurity. Without the pump, the soliton can pass through when the impurity strength is weak; however, it can get trapped when the impurity strength increases. In contrast, we find Thouless pump soliton in Thouless pumps can transit through also for strong impurity strength, and its motion is topologically quantized. Our result explicitly showcases the robustness of topological soliton pumping against microscopic imperfections, and opens a new perspective in the information processing with solitons.