Mass scaling and nonadiabatic effects in photoassociation spectroscopy of ultracold strontium atoms

Abstract

We report photoassociation spectroscopy of ultracold $^{86}\mathrm{Sr}$ atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date: $^{84}\mathrm{Sr},^{86}\mathrm{Sr}$, and $^{88}\mathrm{Sr}$. We attribute that to the recently discovered avoided crossing between the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ ${0}_{u}^{+}$ $({}^{3}{\ensuremath{\Pi}}_{u})$ and ${}^{1}{S}_{0}+{}^{1}{D}_{2}$ ${0}_{u}^{+}$ $({}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available ${0}_{u}^{+}$ and ${1}_{u}$ bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the ${0}_{u}^{+}$ and ${1}_{u}$ curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two $\ensuremath{-}8$-GHz bound states in $^{88}\mathrm{Sr}$ over the previously used model potentials. We show that one of the recently reported energy levels in $^{84}\mathrm{Sr}$ does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients ${C}_{6}({0}_{u}^{+})=3868(50)$ a.u. and ${C}_{6}({1}_{u})=4085(50)$ a.u. are reported.