Signal of Bose-Einstein condensation in an optical lattice at finite temperature

We discuss the experimental signal for the Bose-Einstein condensation of cold atoms in an optical lattice at finite temperature. Instead of using the visibility of the interference pattern via 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-Einstein condensation. We confirm this point with detailed calculations 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