Interference Of Bose-Einstein Condensates In A Spin-dependent Optical Lattice And Tunneling Dynamics Between Two Independent Bose-Einstein Condensates

Bose-Einstein condensation is a new and peculiar matter-form, and has become one of the hotspots of research in contemporary physics. In this thesis, we focus our investigation on the physical mechanism of the interference of Bose-Einstein condensates in a spin-dependent optical lattice, and the tunneling dynamics between two independent Bose-Einstein condensates in a double-well potential. The study on the interference and tunneling of Bose-Einstein condensates may help reveal the macroscopic quantum properties of the condensates and test the fundamental problems of quantum mechanics. Significant new results in this dissertation are shown as below:1. We have presented a theoretical model to investigate the interference of an array of Bose-Einstein condensates loaded in a spin-dependent optical lattice. The mechanism and physical essential of this interference is analyzed and discussed. Our theoretical results agree well with the interference patterns observed in a recent experiment by Bloch group [Phys. Rev. Lett. 91, 010407 (2003)]. In addition, an experimental suggestion of nonuniform phase distribution is proposed to test further our theoretical model and prediction. The present work shows that the entanglement of a single atom is sufficient for the interference of the condensates trapped in a spin-dependent optical lattice and this interference is irrelevant with the phases of individual condensates, i.e., this interference arises only between each condensate and itself and there is no interference effect between two arbitrary different condensates.2. We have investigated theoretically the density distributions and evolution of the spin-dependent atomic wave packets in a harmonic potential. Since the system experiences a Mott insulator transition and a spin-dependent transport before the optical lattice is switched off, the evolution of the atomic wave packets in the harmonic potential is much more complicated than that of the common cases. This experimental proposal presents a new way to test the validity of our theoretical model and prediction.3. An experimental scheme is proposed to study incomplete erasure of which-way information encoded in atomic hyperfine states. Due to the incomplete erasure of the which-way information, it is shown that the interference patterns of the atomic wave...