Quantized nonlinear Thouless pumping

I missed that this interesting theoretical and experimental study of quantized Thouless pumping of solitons was published in Nature last month. The authors were kind enough to share their preliminary results with me while the manuscript was still under review.

Conventional Thouless pumping is defined for linear (non-interacting) energy bands. A quantized topological invariant, the Chern number, describes the translation of a wavepacket's centre of mass due to the periodic modulation, assuming the wavepacket uniformly excites a single energy band of the system.

Recent works have considered the generalization of topological pumping to disordered and interacting quantum systems, including the Thouless pumping of interacting photonic Fock states. But even for interacting quantum systems the time evolution remains governed by a linear Hamiltonian (just in a larger Hilbert space), and so well-developed tools of linear band theory remain applicable.

What is surprising about the present study is that quantized topological pumping can persist for nonlinear wave dynamics, governed by the mean field nonlinear Schrodinger equation. It thus demonstrates that this peculiar phenomenon can be observed in a much wider variety of physical systems than was previously envisaged, including water waves and Bose-Einstein condensates.