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

2001/12/12 by X. B. Wang, K. Matsumoto, Koichi Matsumoto +11
Chemistry · Physics and Astronomy · #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0112071

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

openalex publication_date 2001/12/12 · arxiv created 2002/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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