Quantized topological pumping of solitons in nonlinear photonics and ultracold atomic mixtures.

Exploring the interplay between topological band structures and tunable nonlinearities has become possible with the development of synthetic lattice systems. In this emerging field of nonlinear topological physics, an experiment revealed the quantized motion of solitons in Thouless pumps and suggested that this phenomenon was dictated by the Chern number of the band from which solitons emanate. Here, we elucidate the origin of this nonlinear topological effect, by showing that the motion of solitons is established by the quantized displacement of the underlying Wannier functions. Our general theoretical approach, which fully clarifies the central role of the Chern number in solitonic pumps, provides a framework for describing the topological transport of nonlinear excitations in a broad class of physical systems. Exploiting this interdisciplinarity, we introduce an interaction-induced topological pump for ultracold atomic mixtures, where solitons of impurity atoms experience a quantized drift resulting from genuine interaction processes with their environment.