Ultracold anions for high-precision antihydrogen experiments

Experiments with antihydrogen ($\overline{\text{H}}$) for a study of matter--antimatter symmetry and antimatter gravity require ultracold $\overline{\text{H}}$ to reach ultimate precision. A promising path towards anti-atoms much colder than a few kelvin involves the pre-cooling of antiprotons by laser-cooled anions. Due to the weak binding of the valence electron in anions - dominated by polarization and correlation effects - only few candidate systems with suitable transitions exist. We report on a combination of experimental and theoretical studies to fully determine the relevant binding energies, transition rates and branching ratios of the most promising candidate La$^{-}$. Using combined transverse and collinear laser spectroscopy, we determined the resonant frequency of the laser cooling transition to be $\nu = 96.592\,713(91)$ THz and its transition rate to be $A = 4.90(50) \times 10^{4}$ s$^{-1}$. Using a novel high-precision theoretical treatment of La$^-$ we calculated yet unmeasured energy levels, transition rates, branching ratios, and lifetimes to complement experimental information on the laser cooling cycle of La$^-$. The new data establish the suitability of La$^-$ for laser cooling and show that the cooling transition is significantly stronger than suggested by a previous theoretical study.