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Modern Physics Letters B

BERRY PHASES OF A COMPOSITE SYSTEM IN EXTERNAL FIELDS

Hui Zhao, Xuean Zhao, You‐Quan Li

Published Aug 10, 2006• 0 citations
Publisher

Abstract

We apply the perturbation theory to investigate the behavior of the Berry phase of a composite system. The composite system consists of two weakly-coupled spin-½ particles, in which each particle is driven by a varying magnetic field. The result shows that the Berry phase for one subsystem is controlled by the state of the other subsystem. The method can also be used to deal with the effect of a spin environment on a single-particle system if the particle is weakly coupled to the spin environment.

DOI
10.1142/s0217984906011281

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In this work, we study the geometric phases and quantum entanglement of a composite system consisting of two interacting spin-1/2 particles in the presence of an external magnetic field. The conditions for real and complex eigenvalues are derived and discussed. Based on the non-Hermitian Berry phase, we propose the geometric phase of projective quantum states, discuss their relationship, and analyze their geometric properties. We expound on how the geometric phase of projective quantum states is contingent upon the coupling strength and the nonreciprocity between two subsystems, illustrating the connection between the geometric phase of the composite system and the geometric phases of its subsystems. By studying the quantum entanglement of the subsystems, the role of the correlation between the subsystem and the nonreciprocity is discussed. The results show that the quantum entanglement is influenced and determined by the nonreciprocity of the coupling. These schemes can provide a way to manipulate the nonreciprocal correlation between the subsystems to control the non-Hermiticity, geometric phase, and entanglement of the subsystems.