Bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without flat bands

TL;DR

This paper presents a method to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices without requiring flat bands, using common s-wave interactions and adiabatic state preparation.

Contribution

It introduces a practical scheme to generate fractional quantum Hall states in ultracold atoms without flat bands, utilizing lattice shaking and Feshbach resonance.

Findings

Fractional quantum Hall conductance of 1/2 achieved in shaken honeycomb lattices.

Degenerate ground states with Chern number 1 demonstrated.

Robustness of fractional conductance confirmed during adiabatic state preparation.

Abstract

We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on s-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning on the lattice shaking, and the fractional conductance is robust in the shaken lattice. This provides an easy way to initialize and prepare the fractional quantum Hall states in ultracold-atom platforms, and it paves the way to investigate and simulate strongly correlated quantum matters with degenerate quantum gas.