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International Journal of Theoretical Physics

Geometric Phase for Two Entangled Spin-1/2 Particles in a Magnetic Field

Xuehua Yi, Xin-Ding Zhang

Published Oct 9, 2010• 1 citation
Publisher
DOI
10.1007/s10773-010-0500-5

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The geometric phase for states of two spin-1/2 particles in rotating magnetic field is calculated, in particular, the noncyclic and cyclic non-adiabatic phases for the general case are explicitly derived and discussed. We find that the cyclic geometric phase for the entangled state can always be written as a sum of the phases of the two particles respectively; the same cannot be said for the noncyclic phase. We also investigate the geometric phase of mixed state of one particle in a biparticle system, and we find that the geometric phase for one subsystem of an entangled system is always affected by another subsystem of the entangled system.
The entanglement dependence of Berry's geometric phase is studied in the case of two spin-1/2 particles with a spin-spin interaction.Berry's phases for two spin-1/2 entanglement particles in the presence of spin-spin interaction and noninteraction are calculated,respectively.The expression of calculating geometric phase,when entanglement vanishes,is obtained.Moreover,the geometric phase is discussed when only one of the two particles is affected by the external magnetic field.It is shown that its geometric phase is not equal to that of single particle which is acted by the external magnetic field,and the result is related toαthat affect the strength of entanglement. A general entanglement-dependence geometric phase is formulated.
Above the work of E.Sjoqvist,the geometric phase and the entanglement of the system composed of a pair of noninteracting spin-1/ 2 particles pressing in an external time-independent magnetic field are considered using a new method.The relation between them is gained newly:only if the entanglement is zero will the geometric phase of the composite systems reduce to a sum of one-particle geometric phase.Further more,the Berry's phase and the entanglement of the system composed of a pair of noninteracting spin-1/2 particles pressing in a rotating magnetic field are studied.The same conclusion is gained.