二能级系统严格产生A-A相位的研究

Study on the time-depandent two-level system producing A-A phase

量子循环系统存在着几何相位,求几何相位的实质是求解含时Schr¨od inger方程,而演化算符又是求波函数形式解的最有效方法.以二能级系统为例,计算出该系统的演化算符,进而得到系统的严格演变态,找出系统实现循环演化的两个条件:c ircle条件和循回初态条件,并在各自条件下实现了A-A相,结果表明:循环演化普遍存在于量子体系中,循环演化能否实现由系统来决定,并且对于可实现循环演化的量子系统,A-A相的出现与系统的初始状态有关.

There exists geometric phase in any cyclic evolution of the quantum system. By solving time-dependent Schro dinger equation we can gain the geometric phase, and evolution operator is the most effective method to obtain formal solution of wave function. In this paper, as an example of the two-level-system, by calculating the evolution operator of the two-level-system-satlsfled Schrodinger equation, The two conditions confribute to the system circles, namely, circle condition and cycle initial state condition, and an A-A phase produced under the two conditions in the system is acquired. The results show that any cyclic evolution, related to the system exists universally in the quantum system, and A-A phases are associated with the initial state in the system.