Stark-effect study of excited states in sodium using two-photon spectroscopy

We have used two-photon absorption from counterpropagating laser beams of different frequencies to measure Stark shifts and splittings of the $6{}_{}{}^2{}_{}{}^{}S$, $7{}_{}{}^2{}_{}{}^{}S$, $8{}_{}{}^2{}_{}{}^{}S$, $5{}_{}{}^2{}_{}{}^{}D$, and $6{}_{}{}^2{}_{}{}^{}D$ states in sodium. Beams from a fixed-frequency, single-mode ${\mathrm{Ar}}^{+}$ laser and a tunable, single-frequency cw dye laser were focussed into a coarse sodium atomic beam and the fluorescence was monitored. The collimation of the atomic beam reduced the residual Doppler width inherent in using two different frequencies. Using the two lasers allowed two-photon transitions to be observed at frequencies unattainable with the dye laser alone, and enhanced the transition rates due to the near resonance of the dye laser with the strong Na $3{}_{}{}^2{}_{}{}^{}S\to 3{}_{}{}^2{}_{}{}^{}P$ transition. Our experimental results for the scalar and tensor polarizabilities, ${\alpha }_0$ and ${\alpha }_2$, agree with calculations in the Bates and Damgaard Coulomb approximation within 2% for ${\alpha }_0$ and 9% for ${\alpha }_2$. As a by-product the hyperfine-interaction constants $a$ for the $S$ states and the fine-structure intervals $\delta \nu =\frac{(E_{\frac{3}{2}}-E_{\frac{5}{2}})}{h}$ for the $D$ states were obtained.