Simple method to detect topological Bloch bands in one-dimensional optical lattice

We propose a simple method to detect the Zak phase in one-dimensional optical lattice. This phase is the Berry phase acquired during an adiabatic motion of a particle along closed trajectories in the one-dimensional Brillouin zone, which now has been used to characterize the topological properties of Bloch bands. We show that this phase can be manifested by the shift of the Wannier center in the optical lattice. Through in situ detection of atomic density, the topological properties of the Bloch bands are directly revealed. This method is simple but also general, which could be generalized to detect two-dimensional topological invariants for identification of topological insulators, including the first Chern number and the Z 2 topological index.