Topological quantum pumping, also known as topological charge pumping, represents an important quantum phenomenon that shows the fundamental connection to the topological properties of dynamical systems. Here we introduce a pumping process in a spin-dependent double-well optical lattice with glide symmetry. In the dynamic process, the glide symmetry protects the band-touching points, and topological properties of the system are characterized by the non-Abelian Berry curvature. By engineering a suitable form of coupling between different spin components, the model not only demonstrates topological phase transition but also shows hybridization between the spatial and temporal domain with topological features captured by the Wilson line along the synthetic directions. Our work provides a model based on ultracold atoms towards the implementation of versatile topological matters and topological phenomena in condensed matter systems.

Reference: Topological quantum pumping in spin-dependent superlattices with glide symmetry, Phys. Rev. A 101, 043614 (2020)