Modulational Instability Of Two-component Bose-Einstein Condensates In An Optical Lattice

The modulational instability (MI) is a general phenomenon in the nonlinear systems. This phenomenon can occurred naturally in the homogenous and non-homogeneous media such as in the fluid dynamical mechanics, plasma and nonlinear optics. When the successful realized the Bose-Einstein condensates (BEC) in the experiments, the MI in this system has attracted more and more attentions as the its important meaning in understanding the many nonlinear phenomena such as soliton, domain and superfluid-insulator transition et al.Based on a large of number of theoretical and experimental works on the MI of BECs, the MI of two-component BECs in the optical lattices is analysised. The main contents are as follows:In the first chapter, the background and the recent development in the BECs are reviewed, especially in the nonlinear area.In the second chapter, based on the linear stability analysis, the modulational instability (MI) of two-components Bose-Einstein condensations in the optical lattices is studied. Especially when the condition of atom current conversation is not satisfied, the relation of MI with the different component and modulational wavevectors, and with the inter-and intra-interaction. The results show that the component wavevectors, modulational wavevectors and the interaction between components have great influence on MI of two-component BEC in the optical lattice. This gives us some useful information for manipulating two-component BECs in practice.