Nonlinear Thouless Pumping: Solitons and Transport Breakdown

One-dimensional topological pumping of matter waves in two overlaid optical lattices moving with respect to each other is considered in the presence of attractive nonlinearity. It is shown that there exists a threshold nonlinearity level above which the matter transfer is completely arrested. Below this threshold, the transfer of both dispersive wave packets and solitons occurs in accordance with the predictions of the linear theory; i.e., it is quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of the transport is also explained by nontrivial topology of the bands. In that case, the nonlinearity induces Rabi oscillations of atoms between two (or more) lowest bands. If the sum of the dynamical Chern numbers of the populated bands is zero, the oscillatory dynamics of a matter soliton in space occurs, which corresponds to the transport breakdown. Otherwise, the sum of the Chern numbers of the nonlinearity-excited bands determines the direction and magnitude of the average velocity of matter solitons that remain quantized and admit fractional values. Thus, even in the strongly nonlinear regime the topology of the linear bands is responsible for the evolution of solitons. The transition between different dynamical regimes is accurately described by the perturbation theory for solitons.

Automated summary

This study investigates the one-dimensional topological pumping of matter waves in two overlaid optical lattices with attractive nonlinearity. It reveals that there is a threshold nonlinearity level where matter transfer completely halts. Below this threshold, both dispersive wave packets and solitons follow the predictions of linear theory, quantized and determined by the linear dynamical Chern numbers of the lowest bands. The breakdown of transport is justified by the nontrivial topology of the bands, where nonlinearity induces Rabi oscillations of atoms between the lowest bands. The direction and magnitude of the average velocity of matter solitons, which remain quantized and allow fractional values, are determined by the sum of the Chern numbers of the nonlinearity-excited bands. The study emphasizes the role of the topology of linear bands in the evolution of solitons, even in the strongly nonlinear regime. The transition between different dynamical regimes is accurately described by perturbation theory for solitons.