Four-component full relativistic study on the spectroscopic properties and direct laser cooling schemes for the PbH, PoH, BiH+, and AtH+ molecules

The pseudo-closed transition with enough large Frank-Condon factor (FCF) is a necessary condition for direct laser cooling molecules, which means that only a few molecules with the appropriate ground and excited electronic states can be considered as potential candidates. The electronic and spectroscopic properties of five Ω states are evaluated for the PbH, PoH, BiH+, and AtH+ molecules based on the four-component full relativistic calculations with all-electron basis sets, by which we construct optical schemes for these molecules by using the X12Π1/2 (ν'') ↔ X22Π3/2 (ν') transitions for PbH and BiH+ or the X12Π3/2 (ν'') ↔ X22Π1/2 (ν') ones for PoH and AtH+. The built schemes can provide 104 ∼ 105 scattering phonons with three or five pumping lasers. Moreover, the Doppler/recoil temperatures are 2.08 × 10−3/0.04, 2.91 × 10−3/0.11, 7.48 × 10−3/0.08 and 0.01/0.18 μK, respectively, which means that the temperature of the order of nanokelvin for the PbH and PoH and microkelvin for the BiH+ and AtH+ molecules may be cooled based on the present optical schemes.