Rapid-cycle Thouless pumping in a one-dimensional optical lattice

An adiabatic cycle around a degeneracy point in the parameter space of a one-dimensional band insulator is known to result in an integer valued noiseless particle transport in the thermodynamic limit. Recently, it was shown that in the case of an infinite bipartite lattice the adiabatic Thouless protocol can be continuously deformed into a fine tuned finite-frequency cycle preserving the properties of noiseless quantized transport. In this paper, we numerically investigate the implementation of such an ideal rapid-cycle Thouless pumping protocol in a one-dimensional optical lattice. It is shown that the rapidity will cause first order corrections due to next-to-nearest-neighbour hopping and second order corrections due to the addition of a harmonic potential. Lastly, the quantization of the change in center of mass of the particle distribution is investigated, and shown to have corrections in the first order of the potential curvature.