Visualizing topological orders through Zitterbewegung in ultracold atoms

Topological Haldane model recently has been experimentally realized with ultracold atoms. The low energy Hamiltonian in the model can be formally described by the Dirac equation. In this paper, we explore the Zitterbewegung effect of the Dirac quasiparticles in the vicinity of the two nonequivalent Dirac points in the Haldane model. Through analytical and numerical calculation of the evolution of Gaussian wave packets, we find that the Zitterbewegung patterns could be used to characterize the topological phases of the Haldane model. Since the patterns can be detected through standard time-of-flight measurements, our proposal provides a promising scheme to directly visualize the topological phases in ultracold atoms.