More on nonlinear Thouless pumping

A follow-up to my earlier summary on the experimental observation of quantized nonlinear Thouless pumping.

A few theoretical groups have now posted preprints to arXiv proposing explanations for this effect:

The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps, by two of the authors of the original experimental study, focuses on the weakly nonlinear limit. By rewriting the governing discrete nonlinear Schrodiner equation in the basis formed by the lattice's Wannier functions, the weakly nonlinear dynamics in the complex topological lattices reduces to that of a simple 1D lattice, in which the nonlinear modes are peaked at the centre of the Wannier functions. Thus, the pumping of the solitons follows from the pumping of the linear Wannier functions, which is protected and quantized by the Chern number. Using their theory, the authors design and simulate a soliton pump in a two-dimensional lattice.

Quantized transport of solitons in nonlinear Thouless pumps: From Wannier drags to topological polarons also uses the Wannier function picture to explain the quantization of nonlinear pumping for weak mean-field nonlinearities. In addition, the authors analyze the underlying quantum model (from which the nonlinear Schrodinger equation is obtained by taking the mean field limit) of a Bose gas strongly interacting with massive impurities. Strong coupling between the Bose-gas results in formation of a quasi-particle (Bose polaron), which also exhibits stable quantized pumping.

Nonlinear Thouless pumping: solitons and transport breakdown, submitted before publication of the Nature paper, uses the Wannier function representation to understand the strongly nonlinear limit. In the Wannier basis high power solitons are a superposition of Wannier functions from multiple bands. In this case, the energy difference between the constituent bands leads to a rapid oscillatory motion of the wavepacket during the pumping cycle, superimposed with a slower (average) drift. The average drift speed is quantized by the sum of the bands' Chern numbers. The transition between the low and high power pumping is sharp, occurring as a nonlinear bifurcation (also reported in the experimental paper).