Spectroscopic properties and laser cooling feasibility with the X1∏21/2↔X2∏23/2 transition for the PbX (X = F, Cl, Br, and I) molecules

Abstract

The highly diagonal Frank–Condon factors (FCFs) are necessary for the laser cooling scheme, which means that only the molecules with the appropriate ground and excited electronic states can become candidates. Here, the laser cooling feasibility of the PbX (X = F, Cl, Br, and I) molecules is explored through four-component relativistic calculations. The potential energy curves and transition dipole moments of five Ω states are calculated and used to solve the Schrödinger equation of nuclear motion to obtain the rovibrational energy levels, spectroscopic parameters, the Einstein coefficients, and FCFs. Using the X1 2Π1/2 ↔ X2 2Π3/2 transition with highly diagonal FCFs, we construct optical schemes that can provide 104 ∼ 105 scattering phonons with four pumping lasers for PbX. The Doppler/recoil temperatures of PbX are 419.05 / 57.55, 9.63 / 61.20, 4.95 / 49.98, and 0.71 / 40.17 nK, respectively. Since the 10−4 s of the long spontaneous emission lifetime, the temperatures below microkelvin orders of magnitude can be achieved only if the adequate pre-cooling temperature is satisfied.