Combined experimental and theoretical study of the $6p{}^2{P}_j\to 8s{}^2{S}_{1/2}$ relative transition matrix elements in atomic Cs

A combined experimental and theoretical study of transition matrix elements of the $6p{}^2{P}_j\to 8s{}^2{S}_{1/2}$ transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an $\approx 200{\mathrm{cm}}^{-1}$ range on the low-frequency side of the $6s{}^2{S}_{1/2}\to 6p{}^2{P}_{3/2}$ resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance $6s{}^2{S}_{1/2}\to \mathrm{np}{}^2{P}_j\to 8s{}^2{S}_{1/2}$ transitions. In addition, as the measured quantities are ratios of polarization-dependent intensities at a single-excitation frequency, they are quite insensitive to a variety of common-mode systematic effects; matrix-element ratios may then be determined to high accuracy. In the past, the matrix-element dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the $6p{}^2{P}_j\to 8s{}^2{S}_{1/2}\mathrm{}(j=1/2,3/2\mathrm{})\mathrm{}$ transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).