We have used two-photon absorption from counterpropagating laser beams of different frequencies to measure Stark shifts and splittings of the
62S,
72S,
82S,
52D, and
62D states in sodium. Beams from a fixed-frequency, single-mode
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 $3^{2}S\ensuremath{\rightarrow}3^{2}P$ transition. Our experimental results for the scalar and tensor polarizabilities, ${\ensuremath{\alpha}}_{0}$ and ${\ensuremath{\alpha}}_{2}$, agree with calculations in the Bates and Damgaard Coulomb approximation within 2% for ${\ensuremath{\alpha}}_{0}$ and 9% for ${\ensuremath{\alpha}}_{2}$. As a by-product the hyperfine-interaction constants
a for the
S states and the fine-structure intervals $\ensuremath{\delta}\ensuremath{\nu}=\frac{({E}_{\frac{3}{2}}\ensuremath{-}{E}_{\frac{5}{2}})}{h}$ for the
D states were obtained.
We report here the first experimental demonstration of Doppler-free three-photon spectroscopy. The Doppler broadening is eliminated by insuring that the sum of the momenta of the three photons simultaneously exchanged between the atom and the laser beams is equal to 0. This is accomplished by making a proper choice of the angles between the three exciting beams. The observation has been made on the sodium $3{S}_{\frac{1}{2}}\ensuremath{-}3{P}_{\frac{1}{2}}$ transition with absorption of two photons and induced emission of one.