Floquet band engineering with Bloch oscillations

TL;DR

This paper introduces a method to engineer Floquet bands in driven lattice systems using Bloch oscillations, enabling control over band structure and topology through frequency ratio tuning, with applications demonstrated via Thouless pumping.

Contribution

It presents a novel approach to Floquet band engineering by combining periodic driving with linear potentials, allowing extensive tunability of band topology and structure.

Findings

Floquet bands can be made almost flat or topologically nontrivial with large Chern numbers.

Band structure and topology are tunable by adjusting the frequency ratio.

Thouless pumping confirms the connection between topological properties and Floquet bands.

Abstract

This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-Andr\'e-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands or Floquet bands with large Chern numbers due to the interplay between the periodic driving and Bloch oscillations can be obtained, with the band structure and topology extensively tunable by adjusting the ratio of two competing frequencies. To confirm our finding, we further execute the Thouless pumping of one and two interacting bosons in such a lattice system and establish its connection with the topological properties of single- and two-particle Floquet bands.