周期磁场中具有“令人困惑”简并的Happer模型的拓扑数
Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field
摘要：
Happer模型是Rabi-Breit模型的变体，它描述了${}^{87}\text{Rb}$三重态二聚体分子的总核自旋和总电子自旋-1之间的相互作用。哈珀模型的一个有趣的物理结果是它令人困惑的简并性。本文研究了在周期性磁场作用下电子自旋的Happer模型的拓扑性质。具体地说，我们计算了系统的陈数，无论是对于非退化和退化的情况。我们发现，陈数是密切相关的系统的总角动量，而不是电子自旋。此外，还引入了微扰自旋轴相互作用项，以检测微扰对相应拓扑陈数的影响。最后，在动量空间中，我们从拓扑数的意义上比较了拓扑半金属和Happer模型。在这种模型中，出现了类似“静磁屏蔽”的现象。
英文摘要：
The Happer model, as the variation of Rabi-Breit model, describes the interactions between the total nuclear spin and the total electron spin-1 of the triplet dimer molecules of ${}^{87}\text{Rb}$. One interesting physical consequence of the Happer model is its puzzling degeneracy. In this paper, under the periodic driven magnetic field on total electron spin, the topological properties of the Happer model are present. Specifically, we calculate the Chern number of the system, both for the non-degenerate and degenerate cases. We show that the Chern number is closely related to the total angular momentum of the system, instead of the electron spin. Furthermore, the perturbing spin-axis interaction term is also introduced for detecting the influence on the corresponding topological Chern number. At last, in momentum space, we compare the Happer model with the topological semimetal in the sense of topological numbers. In such model, a "magnetostatic shielding" --like phenomena occurs.
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