Matrix-element spectroscopy of the 5s $^{2}S_{1/2}$ $\rightarrow$ 5p $^{2}P_{j}$ $\rightarrow$ 5d $^{2}D_{j'}$ transitions in $^{87}$Rb

Recent advances in the quality of excited-state transition matrix elements have permitted renormalization of earlier measurements of transition amplitudes associated with the 5s $^{2}S_{1/2}$ $\rightarrow$ 5p $^{2}P_{j}$ $\rightarrow$ 5d $^{2}D_{3/2}$ two-quantum transitions in atomic $^{87}$Rb. Previous measurements were made to high precision, but further reduction of the measurements was limited by uncertainties in data describing the influence of energetically distant transitions. Availability of more reliable matrix elements, including relativistic all-order calculations of transition matrix elements in alkali atoms, has since significantly improved the situation. In the present report, we show that theoretical relative transition amplitudes for the excited state 5p $^{2}P_{j}$$\rightarrow$ 5d $^{2}D_{3/2}$ doublet (ratio= 1.089) are now in excellent agreement with experiment (ratio=1.090). This result, combined with our recent work on cesium, shows that it is possible to determine relative line strengths, for transitions connecting atomic excited states, with precision previously found only in state-of-the-art measurements of alkali resonance doublets. An overview of the experimental technique and supporting data is also presented. Supported by NSF.