不对称外磁场下XXZ型相互作用的两量子比特系统的纠缠

Entanglement of Two Qubits System with XXZ Interaction in the Asymmetry Magnetic Fields

【目的】研究不对称旋转外磁场下两个相互作用的量子比特系统的量子纠缠。【方法】利用数值模拟,得到不对称旋转外磁场下两个相互作用的量子比特系统的4个本征态。为了刻画系统的纠缠,计算了各个本征态的concurrence。【结果】外加旋转磁场的极角以及相互作用的各向异性参数都会对4个本征态的纠缠产生影响。当各向异性参数Δ由0开始增大时,系统的哈密顿量由一种极限下含外场的XX模型经过Δ=1时的海森堡模型逐渐演化为另外一种极限下的Ising模型。【结论】相互作用和外部磁场之间的竞争决定了系统纠缠的演化。通过对系统纠缠的研究,可以对系统在参数的不同区间范围内模型的转化以及本征态的性质有更进一步的认识。

[Purposes]To investigate the entanglement of two qubits system in the asymmetry rotate magnetic fields. [Methods] By using numerical simulation,the four eigenstates of two qubits system in the asymmetry rotate magnetic fields are obtained. To measure the entanglement,the concurrence is calculated. [Findings]Both the polar angle of the rotate magnetic field and the anisotropy parameter of the interaction have important influence to the entanglement for the eigenstates. When the anisotropy parameter is increased from zero to infinity,the Hamiltonian of system will be changed from the XX model to the Heisenberg model,and finally to the Ising model.[Conclusions]The competition between interaction and external magnetic field determines the evolution of entanglement. Through the study of the entanglement,the transition process of the system via the parameter can be obtained and phase transition for the eigenstates can be understood more deeply.