  Recently, optical lattices with non-zero Berry's phases of Bloch bands have
been realized. New approaches for measuring Berry's phases and topological
properties of bands with experimental tools appropriate for ultracold atoms
need to be developed. In this paper, we propose an interferometric method for
measuring Berry's phases of two dimensional Bloch bands. The key idea is to use
a combination of Ramsey interference and Bloch oscillations to measure Zak
phases, i.e. Berry's phases for closed trajectories corresponding to reciprocal
lattice vectors. We demonstrate that this technique can be used to measure
Berry curvature of Bloch bands, the \pi-Berry's phase of Dirac points, and the
first Chern number of topological bands. We discuss several experimentally
feasible realizations of this technique, which make it robust against
low-frequency magnetic noise.
