Quantized transport usually occurs in linear periodic systems with nontrivial topology. While nonlinearity can strongly influence this transport, particularly through the formation of solitons, it is still determined by the spatiotemporal Chern indices of the bands of the underlying linear potential. Here, we show that nonlinear quantized transport can be induced by a sliding nonlinear lattice, even when the latter is combined with a static linear lattice, whose bands are topologically trivial. In such a system, an effective topology emerges from characteristic features of stable Wannier solitons and can be described in terms of the transport of Wannier centers associated with a composite potential combining the stationary linear lattice and an effective moving nonlinear lattice. The phenomenon is generic, as confirmed by the analysis of the continuous Gross-Pitaevskii equation with mutually sliding nonlinear and linear lattices, as well as by the corresponding discrete model with spatially varying coefficients. By increasing the norm of the input state, i.e., the nonlinearity strength, one can observe the unique transition from the absence of transport, to the topological transport, and, eventually, to the nontopological dragging of the input state by the nonlinear lattice.

Close

PrevNext

View figure in article

• Bose-Einstein condensates
• Cold atoms & matter waves
• Optical solitons
• Transport phenomena