High precision measurement of the hyperfine splitting and ac Stark shift of the $7d$ $^{2}D_{3/2}$ state in atomic cesium

We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$ state of $^{133}$Cs using high resolution Doppler-free two-photon spectroscopy in a Cs vapor cell. We determine the hyperfine coupling constants $A = 7.3509(9)$ MHz and $B = -0.041(8)$ MHz, which represent an order of magnitude improvement in the precision. We also obtain bounds on the magnitude of the nuclear magnetic octupole coupling constant $C$. Additionally, we measure the ac Stark shift of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ transition at 767.8 nm to be $-49 \pm 5$ Hz/(W/cm$^2$), in agreement with theoretical calculations. We further report the measurement of collisional shift [$-32.6 \pm 2.0$ kHz/mTorr] and pressure broadening for the individual hyperfine levels of the $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ transition. These measurements provide valuable inputs for analysis of systematic effects in optical frequency standards based on the cesium $6s$ $^{2}S_{1/2} \rightarrow 7d$ $^{2}D_{3/2}$ two-photon transition