Ground State Properties Of Bose-Einstein Condensates In Harmonic Or Anharmonic Traps

Bose-Einstein condensation(BEC) is a ubiquitous phenomenon relating to many fields in physics, such as atomic and molecular physics, quantum optics, quantum statistical physics, condensate matter physics. Since BEC was observed in a remarkable series of experiments on vapors of 87Rb, 23Na, and 7Li in 1995, physicists aimed at gaining a deep insight into the fascinating behavior of this matter. The properties of ground state, interference, bright soliton, dark soliton and vortices are all the hotspot of research. Trapped condensates of alkali-metal atoms are easily accessible to theoretical predictions since the interactions are weak, more rigorous and detailed comparison between theory and experiment would be possible for BEC. Bose-Einstein condensation is a unique phenomenon that all atoms occupy the lowest energy state. The ground state properties of BEC is one of the important object of physicists. In this thesis, we theoretical study the ground state properties of BEC in the harmonic or anharmonic potential. The thesis consists of foreword and four chapters. In the foreword, we mainly introduce the history of BEC research, possible application, simply depict the objective and the content we studied. In chapter 1, we introduce three typical experiments which open a new context for studying the quantum mechanics of mesoscopic systems, the Gross-Pitaevskii and mean-field theory, the computational methods. In chapter 2, By virtue of perturbation method, we investigate the effect of kinetic energy on the ground state of Bose-Einstein condensate. Typical calculation for the 1D 87Rb BEc shows that the amounts of particle number in BEc, corresponding to the cases of strong repulsive limit and noninteracting limit, may be scaled in a new effective regions. In chapter 3, In terms of Gross-Pitaevskii mean-field theory, we present an anharmonic external potential to simulate the ground state properties of the 87Rb atomic Bose-Einstein condensate. Some important results are presented in this chapter. In the final chapter, we summarize the main results and give an outlook of the future study in this field.