Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms

We design an ingenious scheme to realize the Haldane's quantum Hall model without Landau level by using ultracold atoms trapped in an optical lattice. Three standing-wave laser beams are used to construct a wanted honeycomb lattice, where different on-site energies in two sublattices required in the Haldane's model can be implemented through tuning the phase of one of the laser beams. The staggered magnetic field is generated from the Berry phase associated with the atom moving in a region with other three standing-wave laser beams. Moreover, we establish a relation between the Hall conductivity and the equilibrium atomic density upon turning on a stimulated uniform magnetic field, which enables us to detect the topological Chern number with the density profile measurement technique that is typically used in ultracold atoms experiments.