  Since the recent experimental realization of synthetic Rashba spin-orbit
coupling paved a new avenue for exploring and engineering topological phases in
ultracold atoms, a precise, solid detection of Berry phase has been desired for
unequivocal characterization of system topology. Here, we propose a scheme to
conduct momentum-space Aharonov-Bohm interferometry in a Rashba spin-orbit
coupled Bose-Einstein condensate with a sudden change of in-plane Zeeman field,
capable of measuring the Berry phase of Rashba energy bands. We find that the
Berry phase with the presence of a Dirac point is directly revealed by a robust
dark interference fringe, and that as a function of external Zeeman field is
characterized by the contrast of fringes. We also build a variational model
describing the interference process with semiclassical equations of motion of
essential dynamical quantities, which lead to agreeable trajectories and
geometric phases with the real-time simulation of Gross-Pitaevskii equation.
Our study would provide timely guidance for the experimental detection of Berry
phase in ultracold atomic systems and help further investigation on their
interference dynamics in momentum space.
