Thouless Pumping of One-Dimensional Dark Solitons and Domain Walls

Abstract

We predict that quantized transport of dark solitons and domain walls can be observed in mutually sliding optical lattices in both focusing and defocusing nonlinear materials. Two different classes of underlying periodic backgrounds are considered here -- unstaggered and staggered -- which are accurately represented, respectively, by the in-phase and out-of-phase trains of Wannier functions. The nonlinear excitations formed on top of these backgrounds -- dark solitons and domain walls -- are sustained by defocusing or focusing Kerr nonlinearities of the optical medium. Despite non-zero asymptotics, dark solitons and domain walls can still undergo quantized topological transport in dynamically changing refractive index landscape when they and background on which they are constructed are dynamically stable. The extended intervals of propagation constants (and, correspondingly, of the background amplitude) and lattice depths, where stable quantized transport occurs, are identified for both dark solitons and domain walls. Outside these intervals, the quantized transport regime is found to be unstable. Our results extend the concept of nonlinear topological transport from bright to dark soliton states.