一种新的关于两电子纠缠的判据

在海森堡绘景下研究外磁场作用下自旋为1/2的耦合二粒子系统纠缠态问题.用数字方法求解该系统极化矢量随时间变化的微分方程组,得到极化矢量随时间的变化规律.计算结果表明,在合适的外磁场条件下,耦合二粒子可以由自旋平行、总的极化矢量z分量为-2的非纠缠态变为纠缠态;得到由非纠缠态变为纠缠态的最佳外磁场条件;提出根据电子的极化矢量随时间的变化来判断耦合二粒子系统是否达到纠缠态的新方法.本方法不需要采用绝热近似,也适用于更复杂的情况,如存在弛豫的体系.

A new criterion of entanglement of two electrons

The entanglement of two coupling spin 1/2 particles induced by outside magnetic field was studied under Heisenberg picture. By solving the differential equation group of systemic polarization vector varying with time using numerical method, the rule of polarization vector varying with time was obtained. Calculation results reveal that the un-entangled state of two coupling parallel spin 1/2 particles with total polarized vector z component being -2 could translate to entangled state under suitable outside magnetic field condition. The best parameters of outside magnetic field were obtained, and a new method was put forward to judge whether the system of two coupling spin 1/2 particles was in entangled state based on the change of polarization vector with time. This method wasn’t built upon adiabatic approximation, and it is suitable for more complicated situations, such as systems with relaxation.