Direct Measurement of the 5s5p\,{}¹P₁ to 5s4d\,{}¹D₂ Decay Rate in Strontium

We report the first direct experimental determination of the branching ratio of the $5s4d\,{}^1D_2 \to 5s5p\,{}^3P_2$ transition and the decay rate of the $5s5p\,{}^1P_1 \to 5s4d\,{}^1D_2$ transition in neutral strontium. For more than four decades, these quantities lacked an experimental determination independent of theoretical input. We measure the branching ratio to be $0.177(4)$, significantly lower than the widely cited theoretical value of $0.322$ [C. W. Bauschlicher Jr. {\it et al.}, J. Phys. B \textbf{18}, 1523 (1985)]. We also determine the decay rate to be $5.3(5)\times10^3\,\mathrm{s^{-1}}$, consistent with the value reported by Hunter [L. R. Hunter {\it et al.}, Phys. Rev. Lett. \textbf{56}, 823 (1986)] but substantially lower than the recent theoretical prediction of $9.25(40)\times10^3\,\mathrm{s^{-1}}$ [A. Cooper {\it et al.}, Phys. Rev. X \textbf{8}, 041055 (2018)]. These measurements provide an experimental benchmark for quantitative modeling of loss processes in laser cooling and single-atom fluorescence detection in optical tweezers with Sr.