研究了一种基于超导约瑟夫森电路探测非阿贝尔几何相位不对易特征的理论方案, 实现了在宏观量子电路中 对几何相位不对易性的探测。研究结果表明:通过调控外加磁通,体系能够产生两重简并的暗态并自然地诱导了几何相位。 设置两个复合演化过程,考察体系在同一量子态占据几率的差值,可以直接地表征几何相位的不对易特征。 进一步可行性和优势分析表明,该方案具有便易的操控性和较好的量子相干性,从而为实验上研究 非阿贝尔几何相位的不对易特征提供一种有效的途径。

A theoretical scheme is investigated to detect the noncommutative feature of non-Abelian geometric phases with superconducting Josephson circuits. The results show that, two degenerate dark states are generated in the considered system, and the geometric phases are naturally induced through adjusting external fluxes. By designing two composite evolutions and considering the population difference associated with the same quantum state, the noncommutative feature of the geometric phase can be shown directly. Further analyses on the feasibility and advantages indicate that the present scheme possesses the convenient operations and good quantum coherence. Thus the proposal provides an effective approach to experimentally study the noncommutative property of non-Abelian geometric phase.