Investigations Of Localization Properties Of Ultracold Atomic Gases In Optical Field

The ultracold atom gas and Bose-Einstein condensation (BEC) is one of the hot issues in physics. More and more people focus on the manipulation of BEC by using Feshbach resonances driven by light field, which has provided an ideal medium for the localized characteristic of nonlinear systems. In this paper, by using Lagrange variational approach and numerical methods, we start from the nonlinear Schrodinger equation (NLSE) and study matter-wave soliton and Anderson localization in ultracold atomic gases, and do some work in coupling characteristics, the interaction and manipulation of BEC system. These works are summarized as follows:1. The evolution characteristics of coupled BEC matter-wave bright soliton tapped the double-well potentials are investigated. The results show that the system parameters influence on the evolution, switching characteristics and self-trapping behavior of matter-wave solitons. Interactions between the atoms play an important role in the evolution of matter-wave soliton. The soliton's shape changes with the increasing of the linear coupling. Moreover, the interaction between solitons changes with the variety in the degree of coupling, and the self-trapping and Josephson oscillations appear in BEC.2. The evolution and interactions of the linear coupling two-component BEC matter-wave bright soliton are studied in the presence of spatially modulated nonlinearity. The results show that the envelope of the soliton density changes with the spatial variation of the s-wave scattering length. The stable soliton can exist in appropriate initial conditions. The evolution of the solitons depends on the sign and value of the coefficient of the spatially modulated nonlinearity. The nonlinear space management to the condensate can be achieved.3. The dynamic characteristics of the linear and nonlinear coupling BEC matter wave bright solitons trapped an harmonic trap are investigated. The results show that there exist stable solitons and spontaneous oscillation in the condensates under the variant conditions. The stability of the two stationary states is relative to the external trapping potential, the spatially modulated nonlineanty, the number of atoms and the coupled terms. Moreover, we also find that the spatially modulated nonlinearity influences on both the solitons and spontaneous oscillation of atoms in two linearly coupling condensates. The validity of the theoretical predictions is confirmed by the numerical simulation of the coupled equations.4. Starting from the quasi-one-dimensional NLSE, we studied the localization of a weakly interacting BEC in a random speckle. The stability and dilatation of localized states are investigated. Meanwhile, we also studied the effects of the spatially modulated nonlinearity on the shape, energy and localization length of the density envelope. The results show that there exists Anderson localization in the presence of disorder and adiabatic condition, It was found that the nonlinear spatial modulation has influence on the central region and the tail of the localized state.