Signal of Bose condensation in an optical lattice at finite temperature

We discuss the experimental signal for the Bose condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via the time-of-flight imaging, we show that the momentum space density profile in the first Brillouin zone, in particular its bimodal distribution, provides an unambiguous signal for the Bose condensation. We confirm this point with detailed calculation of the change in the atomic momentum distribution across the condensation phase transition, taking into account both the global trapping potential and the atomic interaction effects.