Interference of Bose-condensed gas in a ID optical lattice

For the 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 study the formation of matter-wave interference upon releasing the condensate from the combined potential. The analytical result of the wave function for matter wave interference at any time t is given, and the relation between the interference fringe period and the optical lattice period is obtained. The interference pattern of Bose-condensed gas in the optical lattices is analogous to the multiple slit interference pattern in optics, and coincides with the results of experiment performed by Andrews et al. and Peil et al. and the numerical solution of the G-P equation by Sadhan K. Adhikari.