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Communications in Theoretical Physics

Berry's Phases of the Alkali Atom in a Slowly Changing Strong Magnetic Field and Non-Adiabatic Transition

Chang-Pu Sun, Zhang Linzhi, Qing Xiao

Published Jul 1, 1991• 0 citations
Publisher

Abstract

In this paper the high-order adiabatic approximation (HOAA) method is formulated in a new form so that the calculation is greatly simplified. Using this improved HOAA method, we study the Berry phase effects of the Alkali atom in a slowly-changing strong magnetic field and also the non-adiabatic transitions between the instantaneous angular momentum states. The possible observability is also pointed out.

DOI
10.1088/0253-6102/16/1/73

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In this paper the high-order adiabatic approximation (HOAA) method is formulated in a new form so that the calculation is greatly simplified. Using this improved HOAA method, we study the Berry phase effects of the Alkali atom in a slowly-changing strong magnetic field and also the non-adiabatic transitions between the instantaneous angular momentum states. The possible observability is also pointed out.
In this paper the evolution of a quantum system driven by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation (HOAA) method with Berry's phase, which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized force harmonic oscillator is discussed as an illustrative example.
By invoking the Rabi rotation technique, the Schrödinger wavefunction of a neutral particle with a magnetic moment and a high-spin is exactly solved in a harmonically-changing magnetic field. This result is then applied to illustrate what the accuracy of the quantum adiabatic approximation is exactly and how the non-adiabatic transition vanishes in accompaniment with the appearence of Berry's geometrical phase. The discussion of this paper verifies C. N. Yang's point of view about the generalization of the quantum adiabatic approximation in connection with Berry's phase.