  We calculate the geometric phase associated with the time evolution of the
wave function of a Bose-Einstein condensate system in a double-well trap by
using a model for tunneling between the wells. For a cyclic evolution, this
phase is shown to be half the solid angle subtended by the evolution of a unit
vector whose z component and azimuthal angle are given by the population
difference and phase difference between the two condensates. For a non-cyclic
evolution an additional phase term arises. We show that the geometric phase can
also be obtained by mapping the tunneling equations onto the equations os a
space curve. The importance of a geometric phase in the context of some recent
experiments is pointed out.
