Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps

Nonlinear Thouless pumps for bosons exhibit quantized pumping via soliton motion, despite the lack of a meaningful notion of filled bands. However, the theoretical underpinning of this quantization, as well as its relationship to the Chern number, has thus far been lacking. Here we show that, for low-power solitons, transport is dictated by the Chern number of the band from which the soliton bifurcates. We do this by expanding the discrete nonlinear Schrodinger equation (equivalently, the Gross-Pitaevskii equation) in the basis of Wannier states, showing that a soliton's position is dictated by that of the Wannier state throughout the pump cycle. Furthermore, we describe soliton pumping in two dimensions.

Automated summary

The research reveals that under low-power conditions, the transport of nonlinear Thouless pumps for bosons is influenced by the Chern number of the soliton-separated band. By expanding the equation on the basis of Wannier states, it is demonstrated that the position of the soliton is determined by the position of the Wannier state throughout the pump cycle. Furthermore, soliton pumping in two dimensions is described.