旋转中子及螺旋光纤的几何相

计算得到自旋1/2粒子在旋转磁场下的Bloch方程的严格解及精确波函数,Berry几何相可对演化波函数取绝热极限得到,并将结果与Bitter等的慢中子实验做了比较. 对旋转磁场的一般非绝热循环解,给出了Aharonov-Anandan(AA)几何相和动力学相的解析结果,并用AA几何相理论圆满的解释了有争议的螺旋光纤实验,这项研究证明的关于AA的另一定理表明:对非绝热动力学相取绝热根限时,可得到绝热的动力学相和绝热的几何相. 建议用正交态方法排除绝热近似而获得平行传输条件,从而实现所谓几何量子计算.

GEOMETRIC PHASES FOR HELICAL NEUTRON AND OPTICAL FIBER

The exact wave function and rigorous solution of Bloch equation for spin-1/2 under the rotating magnetic field are obtained in this paper. Berry's geometric phase can be obtained by taking the adiabatic limit on the exact wave function, and be compared with the slow helical neutron experiment done by Bitter et al. For general cyclic solution, the analytic expressions of AA geometric phase and dynamic phase are obtained, and a perfect explanation to a controversial helical optics fiber experiment done by Chiao et al is given. Another theorem in this paper shows that both Berry's dynamic phase and Berry's geometric phase can be obtained by taking the adiabatic limit on the AA dynamic phase. An orthogonal state method is proposed to reach parallel transport, which is practical for the non-adiabatic geometric quantum computation.