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Physical Review A

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

Roberta Hawkins, W. T. Hill, Frank V. Kowalski, ARTHUR L. SCHAWLOW, Sune R. Svanberg

Published Mar 1, 1977• 31 citations
Publisher

Abstract

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 $3^{2}S\ensuremath{\rightarrow}3^{2}P$ 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.

DOI
10.1103/physreva.15.967

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We have measured the fine-structure splitting of the 4d2D4d^{2}D4d2D state of neutral sodium using high-resolution, cw, simultaneous two-photon excitation from the 3s2S3s^{2}S3s2S ground state. Sodium atoms in an atomic beam were excited by a single-mode, cw, tunable dye laser, and the resonance was detected by monitoring the decay fluorescence from the excited state. The fine structure of the 4d2D4d^{2}D4d2D state was well resolved and measured to be ${\ensuremath{\Delta}}_{\mathrm{fs}}=1025\ifmmode\pm\else\textpm\fi{}6$ MHz.
The $3S\ensuremath{-}5S$ transition of Na atoms is induced by absorption of two photons, one each from two circularly polarized beams traveling in opposite directions through the vapor. The beams are derived from a tunable, narrow-band pulsed dye laser. Doppler broadening is absent and the hyperfine structure is resolved. The hyperfine interaction constant A5S{A}_{5S}A5S​ in the 5S5S5S state of the Na23{\mathrm{Na}}^{23}Na23 atom is determined to be 101\ifmmode\pm\else\textpm\fi{}15 MHz.
Two independently tunable, linearly polarized dye lasers are counterpropagated through a heat pipe containing sodium vapor. The frequency of the first laser ${\ensuremath{\omega}}_{1}$ is incremented through both 3p2{p}^{2}p2P1/2{P}_{1/2}P1/2​,3/2 fine-structure levels while the second laser ${\ensuremath{\omega}}_{2}$ is scanned through the energy increment necessary to reach ns 2S1/2^{2}S_{1/2}2S1/2​ and nd2{\mathrm{nd}}^{2}nd2D3/2{D}_{3/2}D3/2​,5/2 levels (n=5--35). Following excitation, ionization occurs through chemi-ionizing collisions. The polarization (defined as the ionization intensity measured when the two planes of polarization of the laser beams are parallel minus the intensity when perpendicular divided by the sum of the intensities) P=(I?{I}_{?}I?​-${I}_{\ensuremath{\perp}}$)/(I?{I}_{?}I?​+${I}_{\ensuremath{\perp}}$) goes from +1 to -1 as ${\ensuremath{\omega}}_{1}$ is tuned between the 3p2{p}^{2}p2P1/2{P}_{1/2}P1/2​,3/2 fine-structure levels. This novel polarization effect is shown to be due to an interference between the two pathways to the ns 2S1/2^{2}S_{1/2}2S1/2​ levels. Upon exciting the unresolved nd 2D3/2^{2}D_{3/2}2D3/2​,5/2 levels, the polarization is very close to zero when ${\ensuremath{\omega}}_{1}$ is at or near the 3p 2P3/2^{2}P_{3/2}2P3/2​,1/2 levels. A simple few-level atom theory reproduces the experimental observations except for the case when both lasers are in resonance.
We have demonstrated the feasibility of Doppler-free two-photon spectroscopy with a train of picosecond standing-wave light pulses from a synchronously pumped mode-locked cw dye laser. The actively controlled mode spectrum provides a means for accurate measurements of large frequency intervals. From a multipulse spectrum of the sodium $3s\ensuremath{-}4d$ transition we have determined a new value of the 4d4d4d fine-structure splitting, 1028\ifmmode\pm\else\textpm\fi{}0.4 MHz.