Nonlinear Thouless pumping: solitons and transport breakdown

TL;DR

This paper investigates how attractive nonlinearity affects topological matter wave pumping in optical lattices, revealing a threshold where transport halts, and explaining the phenomena through band topology and Rabi oscillations.

Contribution

It demonstrates the existence of a nonlinearity threshold that halts topological transport and links nonlinear effects to band topology and soliton dynamics in a novel way.

Findings

Transport is quantized below the nonlinearity threshold.

Above the threshold, transport breaks down due to Rabi oscillations.

The topology of bands influences soliton behavior even in nonlinear regimes.

Abstract

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 wavepackets and solitons occurs in accordance with the predictions of the linear theory, i.e. it is quantized and determined by the dynamical Chern numbers of the lowest band. 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 remains quantized and admits fractional values. Thus, even in 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.