  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.
