# Topological numbers of Happer model with "puzzling" degeneracy in periodic magnetic field

## TL;DR

This paper investigates the topological properties of the Happer model under periodic magnetic fields, revealing a relationship between Chern numbers and total angular momentum, and comparing it to topological semimetals.

## Contribution

It introduces the calculation of Chern numbers for the Happer model in both degenerate and non-degenerate cases under periodic driving, highlighting their dependence on total angular momentum.

## Key findings

- Chern number relates to total angular momentum, not electron spin.
- Perturbing spin-axis interaction affects the topological Chern number.
- Comparison with topological semimetals shows a 'magnetostatic shielding'-like phenomenon.

## Abstract

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.