Three Potential Wells Of The Bose - Einstein Condensate

We investigate the Josephson oscillation and transition to self-trapping for Bose-Eiristein-Condensates(BECs) in a triple-well trap. In Chapter one, we introduce the background and related problems, including the mean-field treatment of BEC system. the classical canonical form of quantum system, the correspondence between classical Hamil-tonian dynamics and BEC system and self-trapping in double well trap. In Chapter two. We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling-law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunnelling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poicare section method that visualizes the motions of BECs in a reduced phase plane. Chapter three is our conclusion.