Nonlinear topological pumping of solitons with time-dependent interactions

Thouless pumping of soliton under cyclic and slow modulation of potential opens a window to understand the interplay between topology and interaction. The dynamics of a soliton change from quantized displacement per pumping cycle to its breakdown to self-trap as time-independent nonlinearity increases. Since nonlinearity can be dynamically and flexibly tuned in ultracold atomic systems, time-dependent nonlinearity can be a new degree of freedom to control behaviors of solitons in a Thouless pump. Leveraging time-dependent nonlinearity, we can not only restore quantized displacement of soliton by avoiding self-crossing structures, but also combine topological pumping and self-trap to effectively realize fractional displacement of soliton per cycle. Surprisingly, even when time translation symmetry is broken by linearly changing nonlinearity, we can still achieve the topological transport of a soliton when the initial soliton is symmetrically distributed. Our work provides a new way for dynamical and topological control of solitons.