Anomalous charge pumping in a one-dimensional optical superlattice

We model atomic motion in a sliding superlattice potential to explore topological "charge pumping" and to find optimal parameters for experimental observation of this phenomenon. We analytically study the band-structure, finding how the Wannier states evolve as two sinusoidal lattices are moved relative to one-another, and relate this evolution to the center of mass motion of an atomic cloud. We pay particular attention to counterintuitive or anomalous regimes, such as when the atomic motion is opposite to that of the lattice.