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Chinese Optics Letters

Geometric phase of spin-1 in a rotating magnetic field

Xiaoyan Zhang, Lian Hu

Published Aug 10, 2006• 1 citation
OpenAlex

Abstract

The quantum phase and the related fields have attracted considerable attention. The geometric phase of spin-1/2 particle in the magnetic field has been discussed comprehensively, but few of spin-1. In this paper, the exact solution of spin-1 was obtained by using rotational frame method. The problems of the Rabi oscillation, dynamical phase, and geometric phase were solved.

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The quantum phase and the related fields have attracted considerable attention. The geometric phase of spin-1/2 particle in the magnetic field has been discussed comprehensively, but few of spin-1. In this paper, the exact solution of spin-1 was obtained by using rotational frame method. The problems of the Rabi oscillation, dynamical phase, and geometric phase were solved.
Quantum invariant theory is an effective method to study geometric phase problems. By making use of the Lewis Riesenfeld invariant theory, a particle with spin j in an oscillating magnetic field is studied and the exact solutions for two different cyclic periods are found. It is then used to obtain two different geometric phases corresponding to two different cyclic periods. It is quite clear from our derivation that the geometric phases corresponding to two different cyclic periods are closely associated with the initial states of the system.