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

TL;DR

This paper numerically investigates rapid-cycle Thouless pumping in a one-dimensional optical lattice, analyzing how finite rapidity affects quantized particle transport and the impact of next-to-nearest-neighbour hopping and harmonic potentials.

Contribution

It demonstrates the feasibility of implementing rapid-cycle Thouless pumping in optical lattices and analyzes the corrections due to non-ideal conditions.

Findings

Rapid-cycle Thouless pumping can be realized in optical lattices.

Corrections due to next-to-nearest-neighbour hopping are significant at high speeds.

Harmonic potential introduces first-order corrections to quantized transport.

Abstract

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.