Quantized transport of solitons in nonlinear Thouless pumps: From Wannier drags to ultracold topological mixtures

Recent progress in synthetic lattice systems has opened the door to novel explorations of topological matter. In particular, photonic devices and ultracold matter waves offer the unique possibility of studying the rich interplay between topological band structures and tunable nonlinearities. In this emerging field of nonlinear topological physics, a recent experiment revealed the quantized motion of localized nonlinear excitations (solitons) upon driving a Thouless pump sequence; the reported observations suggest that the quantized displacement of solitons is dictated by the Chern number of the band from which they emanate. In this work, we elucidate the origin of this intriguing nonlinear topological effect, by showing that the motion of solitons is established by the quantized displacement of Wannier functions. Our general theoretical approach, which fully clarifies the central role of the Chern number in solitonic pumps, provides a rigorous 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.