  In a nondegenerate syste, the abelian Berry's phase will never cause
transitions among the Hamiltonian's eigenstate. However, in a degenerate
syatem, it is well known that the state transition can be caused by the
non-abelian Berry phase. Actually, in a such a system, the phase factor is not
always nonabelian. Even in the case that the phase is a nondiagonal matrix, it
still can be an abelian phase and can cause the state transitions. We then
propose a simple scheme to detect such an effect of the Berry phase to the
degenerate states by using the optical entangled pair state. In this scheme, we
need not control any external parameters during the quantum state evolution.
