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We design an ingenious scheme to realize the Haldane's quantum Hall modelwithout Landau level by using ultracold atoms trapped in an optical lattice.Three standing-wave laser beams are used to construct a wanted honeycomblattice, where different on-site energies in two sublattices required in theHaldane's model can be implemented through tuning the phase of one of the laserbeams. The staggered magnetic field is generated from the Berry phaseassociated with the atom moving in a region with other three standing-wavelaser beams. Moreover, we establish a relation between the Hall conductivityand the equilibrium atomic density upon turning on a stimulated uniformmagnetic field, which enables us to detect the topological Chern number withthe density profile measurement technique that is typically used in ultracoldatoms experiments.

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