Evolution of Matter Wave Interference of Bose-Condensed Gas in a 1D Optical Lattice

For a Bose-condensed gas in a combined potential consisting of an axially-symmetric harmonic magnetic trap and one-dimensional （1D） optical lattice, using the mean-field Gross-Pitaevskii （G-P） equation and the propagator method, we obtain the analytical result of the order parameter for matter wave interference at any time. The evolution of the interference pattern under a variation of the relative phase △Ф between successive subcondensates trapped on an optical lattices is also studied. For △Ф=π, the interference pattern is symmetric with two sharp peaks, which are symmetrically located on a straight line on both sides of a vacant central peak and moving apart from each other. This work is in agreement with available experimental results.