Self-trapping And Macroscopic Quantum Tunneling Of Bose-Einstein Condensates

Under mean-field method and single model approximation, the self-trapping phenomenon and macroscopic quantum tunneling problem of Bose-Einstein condensates are investigated. In an external field, many interesting phenomena are found. Reasonable interpretations for these findings are given with numerical and analytical method.Firstly, with simplest two-component model, we investigate thoroughly the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BEC) in a symmetric double well potential. Using phase space analysis approach, we identify two kinds of self-trapping by their different relative phase behavior: running phase type and oscillating phase type it. With applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, saying, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high and low frequency modulations. For an intermediate frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affects the tunneling dynamics and demonstrates many novel phenomena. We study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.Secondly, for the sake of extending our study to more interesting many-component system, we present a comprehensive analysis of the Landau-Zener tunneling of a nonlinear three-level system. In a linearly sweeping external field, we find the presence of nonzero tunneling probability in the adiabatic limit (i.e., very slowly sweeping field) even for the situation that the nonlinear term is very small and the energy levels keep the same topological structure as that of linear case. In particular, the tunneling is irregular with showing an unresolved sensitivity on the sweeping rate. For the case of fast-sweeping fields, we derive an analytic expression for the tunneling probability with stationary phase approximation and show that the nonlinearity can dramatically influence the tunneling probability when the nonlinear "internal field" resonates with the external field. We also discuss the asymmetry of the tunneling probability induced by the nonlinearity. Physics behind the above phenomena is revealed and possible application of our model to triple-well trapped Bose-Einstein condensate is discussed.In fact, many-component system can be made of spin bose condensates with internal spin degree of freedom, which has been observed in experiments. To compare with these experiments and provide hetter theoretical scheme, we thirdly investigate the spin tunneling of spin-1 Bose-Einstein condensates. In a linearly sweeping magnetic, we focus on the two typical alkali Bose atoms ⁸⁷Rb and ²³Na condensates and study their tunneling dynamics according to different sweeping rates of external magnetic fields. In the adiabatic (i.e., slowly sweeping) and sudden (i.e., fast sweeping) limits, no tunneling is observed. For the case of moderate sweeping rates, the tunneling dynamics is found to be very sensitive to the sweeping rates with showing a chaotic-like tunneling regime. With magnifying the regime, however, we find interestedly that the plottings become resolvable under a resolution of 10^-4G/s where the tunneling probability with respect to the sweeping rate shows a regular periodic-like pattern. Moreover, a conserved quantity standing for the magnetization in experiments is found can dramatically affect the above picture of the spin tunneling. Theoretically we have given a reasonable interpretation to the above findings and hope our studies would bring more attention to spin tunneling experimentally.Finaly, extending the above idea to a five-component system, we give the spin tunneling model of spin-2 bose condensates.