Solution Of G-P Equation Of Bose-Einstein Condensation In 2D Optical Lattice

The realization of Bose-Einstein condensation in a thin and diluted atomic gas hasattracted extensive concern in recent decades. It has provided physicists with a new fertileground for exploring many aspects of this interesting physical phenomenon. Based on themean-field theory, we investigate the Gross-Pitaevskii equation, which describes theBose-Einstein Condensation, making some researches to the problem in the BEC. This papercomprises four parts as follows: chapterâ… : Bose-Einstein condensation, a new state of thematerial is introduced. Including the Bose-Einstein condensation of statistics property and therealization on the experiment, G-P equation of a common Bose-Einstein condensation isobtained and G-P equation of a quasi-2D Bose-Einstein condensation is also obtained.Chapterâ…¡: Simple optical lattices of the relevant knowledge are introduced. The creation ofan optical lattice as well as its properties, familiar optical lattice and potential applications arediscussed. Chapterâ…¢: the properties of BEC with strong interaction to imprison in thecombination power field of the 2D optical lattice and trap field is discussed. Through theestablishment of the model, which satisfies the nonlinear Schrodinger equation. By adjustingthe 2D optical lattice potential to keep it with the interaction of BEC atoms into balance, thusgain a linear Schrodinger equation, solution of the linear equation is obtained. Finally, in thefourth chapter of this paper, we summarized the main results and give an outlook of thefuture study in this field.