Precision measurement of hyperfine constants and isotope shift of the Rb 6S1/2 state via a two-photon transition

Using Doppler-free two-photon spectroscopy of the Rb $5S_{1/2}$ to $6S_{1/2}$ transition in a temperature-controlled vapor cell, for both naturally occurring isotopes, we measure to high accuracy the hyperfine splittings and constants, as well as the isotope shift of the $6S_{1/2}$ state. We lock a tunable microwave-driven electro-optic modulator sideband of the $993\text{−}\mathrm{n}\mathrm{m}$ laser to an ultrastable high-finesse cavity, thus achieving microwave frequency accuracy for the relative laser tuning. The line shapes are fit with a Voigt profile to extract line centers in order to calculate the hyperfine splittings, magnetic dipole hyperfine constants, isotope shift, and hyperfine anomaly. For the hyperfine splittings of the $6S_{1/2}$ state in ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$, respectively, we find $717.195\left(3\right)\mathrm{M}\mathrm{Hz}$ and $1614.709\left(3\right)\mathrm{M}\mathrm{Hz}$. For the hyperfine constants $A$ for the $6S_{1/2}$ states, we find $239.065\left(2\right)\mathrm{M}\mathrm{Hz}$ and $807.355\left(2\right)\mathrm{M}\mathrm{Hz}$ for ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$, respectively, and $-99.189\left(3\right)\mathrm{M}\mathrm{Hz}$ for the isotope shift (${}^{85}\mathrm{Rb}$ minus ${}^{87}\mathrm{Rb}$). These hyperfine splittings and constants are 10 to 25 times more accurate than previously published results. We measure the hyperfine anomaly ${}^{85}\mathrm{\Delta }^{87}$ of the $6S_{1/2}$ state to be $-0.00350\left(1\right)$, which is about 20 times more accurate than previously published results.