In terms of exact solutions of the time-dependent Schrodinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2)coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.Comment: 18 pages,5 figure

In this letter we predict a novel second-order quantum phase transition of twocomponent Bose-Einstein condensates coupled with a periodically driven laser field in the resonant case. It is shown that this quantum phase transition from the normal to the tunneling phases can be controlled by the interspecies nonlinear interaction tuned via the magnetic-field-dependent Feshbach resonance technique. Furthermore, it is also demonstrated that this quantum phase transition can be detected by measuring the ground-state population imbalance between two condensates.