  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.
