Dispersion-suppressed topological Thouless pumping

In Thouless pumping, although a nonflat band has no effects on the quantization of particle transport, it induces wave-packet dispersion which hinders the practical applications of Thouless pumping. Indeed, we find that the dispersion mainly arises from the dynamical phase difference between individual Bloch states. Here we propose two efficient schemes to suppress the dispersion in Thouless pumping: a relocalization echo protocol and a high-order tunneling suppression protocol. In the relocalization echo protocol, we reverse the Hamiltonian in the second pumping cycle to cancel the dynamical phase difference arising from the nonflat band, so that the dispersed wave packet becomes relocalized. In the high-order tunneling suppression protocol, we modulate the nearest-neighbor tunneling to make the Bloch band more flat and suppress the high-order tunneling which causes wave-packet dispersion. Our study paves a way toward the dispersionless Thouless pumping for practical applications in matter transport, state transfer, and quantum communication.