Happer model with puzzling degeneracy in periodic magnetic field. (arXiv:1908.04726v1 [quant-ph])

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. Near the degenerate point, the subspace behaves like a
higher-spin topological semimetal. In such model, a "magnetostatic shielding"
--like phenomena occurs.