Hyperfine quenching of the metastable ${}^{3}P_{0,2}$ states in divalent atoms

Hyperfine quenching rates of the lowest-energy metastable ${}^{3}P_0$ and ${}^{3}P_2$ states of Mg, Ca, Sr, and Yb atoms are computed. The calculations are carried out using ab initio relativistic many-body methods. The computed lifetimes may be useful for designing novel ultraprecise optical clocks and trapping experiments with the ${}^{3}P_2$ fermionic isotopes. The resulting natural widths of the ${}^{3}P_0-{}^{1}S_0$ clock transition are $0.44\text{mHz}$ for ${}^{25}\mathrm{Mg}$, $2.2\text{mHz}$ for ${}^{43}\mathrm{Ca}$, $7.6\text{mHz}$ for ${}^{87}\mathrm{Sr}$, $43.5\text{mHz}$ for ${}^{171}\mathrm{Yb}$, and $38.5\text{mHz}$ for ${}^{173}\mathrm{Yb}$. Compared to the bosonic isotopes, the lifetime of the ${}^{3}P_2$ states in fermionic isotopes is noticeably shortened by the hyperfine quenching but still remains long enough for trapping experiments.

Figure 1

Lowest-lying energy levels of $\text{Mg}\left(n=3\right)$, $\text{Ca}\left(n=4\right)$, $\text{Sr}\left(n=5\right)$, and $\text{Yb}\left(n=6\right)$, relevant to the radiative decay of the $nsnp{}^{3}P_{0,2}$ states. The hyperfine quenching predominantly is caused by the admixture of the $nsnp{}^{3}P_1$ and $nsnp{}^{1}P_1$ states.