A simple way to detect the state transition caused by the nondiagonal abelian Berry phase

Wang, X. B.; Matsumoto, K.; Fan, H.; Tomita, A.; Pan, J. W.

A simple way to detect the state transition caused by the nondiagonal abelian Berry phase

Authors

Description

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.
The evolution of a non-commutative matrix is obtained through the operation in the zero eigenvalue space