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Physical Review A

Collision effects in velocity-selective optical pumping of sodium

C.G. Aminoff, Juha Javanainen, M. Kaivola

Published Aug 1, 1983• 36 citations
Publisher

Abstract

We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The ${D}_{1}$ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: $\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.

DOI
10.1103/physreva.28.722

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Physical Review A•Nov 1, 1982•32 citations
We report on a quantitative experimental investigation of velocity-changing collisions by means of velocity-selective optical pumping (VSOP). We have calculated the VSOP line shape for an atom with hyperfine structure with the use of two phenomenological kernels for the collision effects: the Keilson-Storer kernel, and a two-term kernel consisting of a broad Keilson-Storer part and a narrower Gaussian component. Corrections were included to account for the finite absorption in the sample and the backward reflection of the pumping beam. The experiments were carried out in sodium vapor with neon as the perturber gas. The D1{D}_{1}D1​ line of sodium was used for optical pumping, and the orientation of the ground state was detected. Free parameters of the theory were determined by fitting the predicted line shapes to experimental curves. The Keilson-Storer kernel proved unsatisfactory, but the two-term kernel reproduced well the observed line shapes over the entire collision profiles in the neon pressure range 0-57 mtorr. In an independent experiment using rapidly modulated VSOP we also measured directly the cross section of velocity-changing collisions: \ensuremathσ=(1.13\ifmmode±\else\textpm\fi0.10)\ifmmode×\else\texttimes\fi10\ensuremath−14\ensuremath{\sigma}=(1.13\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\ensuremathσ=(1.13\ifmmode±\else\textpm\fi0.10)\ifmmode×\else\texttimes\fi10\ensuremath−14 cm2{\mathrm{cm}}^{2}cm2. The large weight obtained for the narrow Gaussian from the fits, as well as the collision cross section which is three times as large as the cross section deduced from tabulated gas kinetic radii, may indicate the presence of collisions with relatively small velocity changes in addition to hard-sphere encounters.
We report the results of an experimental study of the effects of velocity-changing collisions on two-photon and stepwise-absorption line shapes. Excitation spectra for the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}\ensuremath{\rightarrow}4{D}_{\frac{1}{2}}$ transitions of sodium atoms undergoing collisions with foreign gas perturbers are obtained. These spectra are obtained with two cw dye lasers. One laser, the pump laser, is tuned 1.6 GHz below the $3{S}_{\frac{1}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ transition frequency and excites a nonthermal longitudinal velocity distribution of excited 3P123{P}_{\frac{1}{2}}3P21​​ atoms in the vapor. Absorption of the second (probe) laser is used to monitor the steady-state excited-state distribution which is a result of collisions with rare gas atoms. The spectra are obtained for various pressures of He, Ne, and Kr gases and are fit to a theoretical model which utilizes either the phenomenological Keilson-St\"orer or the classical hardsphere collision kernel. The theoretical model includes the effects of collisionally aided excitation of the 3P123{P}_{\frac{1}{2}}3P21​​ state as well as effects due to fine-structure state-changing collisions. Although both kernels are found to predict line shapes which are in reasonable agreement with the experimental results, the hard-sphere kernel is found superior as it gives a better description of the effects of large-angle scattering for heavy perturbers. Neither kernel provides a fully adequate description over the entire line profile. The experimental data is used to extract effective hard-sphere collision cross sections for collisions between sodium 3P123{P}_{\frac{1}{2}}3P21​​ atoms and helium, neon, and krypton perturbers.
Measurements of velocity-changing collision (VCC) kernels are obtained using velocity-selective optical pumping. This is the first measurement of the shape of an elastic VCC kernel over the full thermal range of velocity changes. Since ground-state collisions are studied (5s1/2{\mathit{s}}_{1/2}s1/2​ Rb and He, Ne, Ar, Kr, or Xe), very low buffer-gas pressures can be used, and therefore pressure broadening (dephasing collisions) does not obscure the effects of VCC's. The data are deconvolved to eliminate the effects of the natural linewidth and are then extrapolated with respect to buffer-gas pressure to determine the single-collision limit. For small initial velocities, the measured kernels are consistent with a hard-sphere model for large velocity changes, but differ significantly for small velocity changes. The measured VCC kernels for large initial velocities and large velocity changes do not exhibit this agreement with the hard-sphere kernel. This implies that information about the inter- atomic potential can be obtained from a measurement of VCC kernels. We also show the inadequacy of the much-used Keilson-Storer kernel [J. Appl. Math. 10, 243 (1952)].
We report on an experimental investigation of the collision kernels governing the effects of velocity-changing collisions, fine-structure-changing collisions, and their interplay, for Na--noble-gas pairs. The velocity distributions in the two Na excited-state fine-structure levels and in the Na ground-state hyperfine levels have been measured in the presence of a pump laser which produces velocity-selective excitation. For interpretation of these experiments we use a rate-equation model developed in the context of light-induced drift: the velocity-changing collisions are accounted for by a composite Keilson-Storer kernel describing large-angle and small-angle collisions and the fine-structure-changing collisions are treated in the sudden limit. The model is valid for arbitrarily high pump laser intensities and uses only a single adjustable parameter characterizing the small-angle scattering. It is found that the theory describes the experimental velocity distributions in all four Na levels over a wide range of experimental parameters for each Na--noble-gas pair. The relevance of the collision kernels deduced in the present work is discussed in the context of light-induced drift.
We extend the theory of velocity-selective laser optical pumping in atomic vapors, allowing for arbitrarily rapid velocity-changing collisional rates. The results yield a simple relationship between the line-shape areas of narrow spectroscopic features present in optically pumped samples. This relationship gives directly the ground- and excited-state velocity-changing collision rates and cross sections. We use the results to analyze the data from a laser optical-pumping experiment in 6Li^{6}\mathrm{Li}6Li vapor perturbed by Ar buffer gas.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
We have observed that spectral lines obtained in sodium vapor can be strongly distroted when using two-photon spectroscopy with a resonant intermediate state. In some cases, the spectral lines appear to be split into two components. We demonstrate that these effects are due to velocity-selective optical pumping of the atomic ground state; the line shapes reflect the velocity distribution of atoms in the excited intermediate state. We have analyzed the effects using the time-dependent solutions of the rate equations which describe the time evolution of optical pumping for the various atomic velocity groups, and we obtain good agreement with experiment. Optical-pumping problems are often analyzed with the use of steady-state rate equations which incorporate phenomenological relaxation; such approaches are not capable of describing our observations. Velocity-changing collisions are shown to suppress the effects and they explain why these effects were not previously observed; the previous experiments were carried out with slight amounts of a buffer gas in the vapor cell. The effects reported here must be accounted for when carrying out laser-induced line-narrowing experiments in atoms or molecules that can be optically pumped; they can also be used as a new and more sensitive probe of optical pumping in vapors.