自旋为1/2的Abel Wu-Yang单极子的量子模拟
Quantum simulation of Abelian Wu-Yang monopoles in spin-1/2 systems
摘要：
借助于Berry曲率和第一陈数$($ $\textit{C}_1$ $)$，我们对超导量子比特哈密顿量参数空间中的人工磁单极子进行了解析和数值模拟.自旋为1/2的$($量子比特$)$的拓扑结构可以用描述哈密顿量本征态几何的Berry曲率分布来描述。参数空间中的简并点充当磁场的源$($ $\textit{C}_1$ = $1$ $)$或汇$($ $\textit{C}_1$ = $-1$ $)$。我们注意到Berry曲率$)$所描述的磁场$($的强度对拓扑跃迁过程中的量子态有明显的影响。当简并点从外到内再到系统参数所覆盖的流形之外时，它表现出一个不寻常的性质，即量子态的跃迁是非对称的。我们的结果也为探索其他自旋1/2系统中磁单极子的有趣性质铺平了道路。
英文摘要：
With the help of the Berry curvature and the first Chern number $($$\textit{C}_1$$)$, we both analytically and numerically investigate and thus simulate artificial magnetic monopoles formed in parameter space of the Hamiltonian of a driven superconducting qubit. The topological structure of a spin-1/2 system $($qubit$)$ can be captured by the distribution of Berry curvature, which describes the geometry of eigenstates of the Hamiltonian. Degeneracy points in parameter space act as sources $($$\textit{C}_1$ = $1$$)$ or sinks $($$\textit{C}_1$ = $-1$$)$ of the magnetic field. We note that the strength of the magnetic field $($described by Berry curvature$)$ has an apparent impact on the quantum states during the process of topological transition. It exhibits an unusual property that the transition of the quantum states is asymmetric when the degenerate point passes from outside to inside and again outside the manifold spanned by system parameters. Our results also pave the way to explore intriguing properties of magnetic monopoles in other spin-1/2 systems.
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