The groud-state wave function and evolution of the interference pattern for a Bose-condensed gas in 3D optical lattices

Abstract

Based on the Gross-Pitaevskii equation and by using the effective chemical poten tial,we study the distribution of the Bose-condensed gas in the combined potenti als (magnetic trap and three-dimensional optical lattices).The normalized ground-state wave function is given from the distribution of the Bose-condensed gas.The analytical expression of the density distribution of the Bose-condensed gas is given by using the propagator method when the combined potentials and only the optical lattices are switched off,respectively.When the combined potentials are switched off,the theoretical results of this work agree well with the experiment by Greiner et al.When only the optical lattices are switched off,it is show n that the interference pattern will oscillate in the magnetic trap.In addition,the evolution of the interference pattern is also investigated in the case of an isotropic magnetic trap.