Quantum Tunneling Of Multi-component BEC

The experimental realization of Bose-Einstein condensate has attract lots of interest in investigating various quantum phenomena within, quan-tum tunneling effect is one of the hot topic in the last decades. This thesis is devoted to study quantum tunneling problem in multicomponent Bose-Einstein condensates(BEC). Their are two systems we deal with, one is a binary mixtures of BEC trapped in double well, the other is a spin-1 Bose-Einstein condesates. Both system show interesting tunneling phenomena, one is tunneling between different wells, while the other show internal tun-neling. We first introduce the basic knowledge of Bose-Einstein condensate, then the models in our context of investigation.In chapter II, we disscussed the dynamical phase transition in sys-tem of double well trapped one-species BEC. Considering the first order quantum correction by using'Bogoliubov backreaction method" (BBR), we find the effect of quantum fluctuation would change behavior of the transition from Josephson oscillation to self-trapping. First, it is not a critical phenomena anymore. Second, the phase transition point has been shifted. Third, we find the Von Neumann entropy will reach its maximum at the original dynamical phase transition point.In chapter III, we disscussed the dynamical phase transition in sys-tem of double well trapped two-species BEC. We find that by gradually increasing the interspecies interaction strength, there exists a dynamical phase transition which involves logarithmic singularity. This dynamical phase transition is the direct consequence of separatrix crossing in phase space as we revealed by using the poincare section analysis, this is quite similar to the Josephson oscillation to self-trapping transition found in one species double well problem. In chapter IV, we extended the "Bogoliubov backreaction method" (BBR) to the problem of double well trapped two-species BEC, and we disscussed the first order quantum correction on dynamical phase transition behavior described in previous chapter.In chapter V, considering the domain formation influences, we diss-cussed internal tunneling behavior of a spin-1 BEC system. We demon-strate that the domain formationis a co-effect of the quantum coherence and the thermal relaxation. Also, a thermally enhanced quantum-oscillation is observed during the dynamical process of the domain formation, and it is found the spatial separation of domains leads to significant decay of the MF= 0 component fraction in an initial MF=0 condensate.A summary was made in the last chapter.