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Physical Review A

Role of adiabaticity in controlling alkali-metal fine-structure mixing induced by rare gases

Ben Eshel, Joseph A. Cardoza, David E. Weeks, Glen P. Perram

Published Apr 20, 2017• 10 citations
Publisher

Abstract

The collision cross sections for alkali-metal--rare-gas spin orbit mixing between the ${n}^{2}{P}_{3/2}\ensuremath{\rightarrow}{n}^{2}{P}_{1/2}$ levels trend strongly with the Massey parameter, or adiabaticity of the collisions. The strength of the interaction, as characterized by the ${C}_{6}$ dispersion coefficient, is a secondary influence on the rates. An analytic expression for the probability of energy transfer in alkali-metal--rare-gas collisions is derived using time-dependent perturbation theory. The model agrees well with a broad literature survey of the observed temperature-dependent cross sections. A simple interaction potential successfully organizes the alkali-metal--rare-gas database. The rates become very large for high-lying states, as the collisions are quite sudden and the radius of the valence electron is large. In contrast, the highly adiabatic cesium ${6}^{2}P$ mixing rates are six to eight orders of magnitude smaller. The mixing rate for the Rb-He diode pumped alkali laser system varies from $0.20--1.53\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\mathrm{cm}{}^{3}/\mathrm{at}.\phantom{\rule{0.16em}{0ex}}\mathrm{s}$ for $T=279--893\phantom{\rule{0.222222em}{0ex}}\mathrm{K}$.

DOI
10.1103/physreva.95.042708

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Fine-structure mixing cross-sections for the alkalis in collisions with the rare gases are reviewed. Included in the review are all the rare gases in collisions with all of the first excited state of the alkalis, the second excited state for K, Rb and Cs and the third excited state for Rb and Cs. The cross-sections are converted to probabilities for energy transfer using a quantum-defect calculated cross-section and are then presented as a function of adiabaticity. The data shows a clear decreasing trend with adiabaticity but secondary factors prevent the probabilities from decreasing as quickly as expected. Polarizability is introduced as a proxy for the secondary influences on the data as it increases with both rare gas partner and alkali excited state. The polarizability is shown to cause the probability of fine structure transition to be higher than expected. An empirical model is introduced and fit to the data. Future work will develop a model using time-independent perturbation theory in order to further develop a physical rational for the dependence of fine structure cross sections on adiabaticity and to further understand the secondary influences on the probability for fine structure transition.
For years, inelastic, fine-structure-changing collisions between excited alkali-metal atoms and noble-gas perturbers have been a source of information on the alkali-metal--noble-gas interaction. Here, we consider the role of elastic fine-structure-mixing collisions on alkali-metal absorption cross sections. Specifically, we consider the four optical hyperfine transitions of the D1{D}_{1}D1​ absorption spectrum for 87Rb^{87}\mathrm{Rb}87Rb, and in particular the doublet corresponding to $5^{2}S_{1/2}({F}_{g}=2)\ensuremath{-}5^{2}P_{1/2}({F}_{e}=1,2)$ transitions. Although ideally the amplitudes of the doublet's absorption cross sections are identical, we find that fine-structure mixing of D2{D}_{2}D2​ oscillator strength into the D1{D}_{1}D1​ spectrum breaks the cross sections' equality and leads to doublet asymmetry. We obtain a fine-structure mixing parameter $\ensuremath{\lambda}$ of $(5.4\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{3}$, and estimate a 52P1/25^{2}P_{1/2}52P1/2​ hyperfine-splitting density shift $\ensuremath{\zeta}$ in the 87Rb^{87}\mathrm{Rb}87Rb-Xe system of $+0.71\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}/\mathrm{amagat}$. These results have implications for spectroscopic applications of the 87Rb^{87}\mathrm{Rb}87Rb isoclinic point, which we consider as part of our conclusions.
Pulsed excitation on the two-photon Cs $6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}7{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2,5/2}$ transition results in time-resolved fluorescence at 697 and 672 nm. The rates for fine-structure mixing between the 72D3/2,5/27{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2,5/2}72D3/2,5/2​ states have been measured for helium and argon rare-gas collision partners. The mixing rates are very fast, $1.26\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9} {\mathrm{cm}}^{3}$/atom s for He and $1.52\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{cm}}^{3}$/atom s for Ar, driven by the small energy splitting and large radial distribution for the valence electron. The quenching rates are considerably slower, $6.84\ifmmode\pm\else\textpm\fi{}0.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $2.65\ifmmode\pm\else\textpm\fi{}0.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11} {\mathrm{cm}}^{3}$/atom s for He and Ar, respectively. The current results are placed in context with similar rates for other alkali-metal--rare-gas collision pairs using adiabaticity arguments.
The cross sections for rubidium $5^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}5^{2}P_{\frac{3}{2}}$ and cesium $6^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}6^{2}P_{\frac{3}{2}}$ excitation transfer due to inert-gas collisions have been measured. The temperature of the collision vessel has been varied from 300\ifmmode^\circ\else\textdegree\fi{}K to 900\ifmmode^\circ\else\textdegree\fi{}K in order to partially establish the velocity dependence of these cross sections (the alkali resonance-line optical depths were always much less than 1). The various cross sections exhibit a systematic behavior that can be combined to find the general shape of a "universal" cross section that ranges across six orders of magnitude, starting just below the threshold for "sudden" collisions. The surprisingly large influence of optical line broadening on these excitation-transfer measurements has been removed as a source of error.
The spin relaxation of optically pumped rubidium vapor induced by rubidium-rare-gas atomic collisions has been investigated in an ultraclean environment. The experiment was performed under conditions such that the partial pressure of nonrare-gas impurities was less than 1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ Torr, and that the time between Rb-Rb spin exchange collisions was short compared to the spin relaxation time. The cross sections (in cm2{\mathrm{cm}}^{2}cm2) for disorientation of rubidium were found to be: He, 3.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}25}$; Ne, 3.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$; Ar, 1.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$; Kr, 7.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}21}$; Xe, 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}19}$. The fact that these cross sections are considerably smaller than previously reported values is attributed primarily to the low degree of impurity contamination in the present work. When compared with already existing values for cesium and sodium, the disorientation cross sections of these three alkali metals are seen to have a remarkably similar dependence on buffer-gas atomic number. The new experimental values are also compared with recent theoretical calculations.
The J-mixing process of alkali-metal atoms in thermal collisions with noble-gas atoms has been a nemesis due to the fact that the process is a complicated three-body collision process. Since current theoretical methods treat the collision process as a two-body one by ignoring the interaction between the perturber noble-gas atom and the alkali-metal atomic core, their results do not agree with experiments, especially in lower-n states and for heavier noble-gas atoms. Within the framework of an eikonal approximation in this paper, we have presented a theoretical description of the J-mixing process of alkali-metal atoms. Our present work shows that the direct contribution to the process from the interaction between the perturber atom and the alkali-metal atomic core is negligible, but the interaction makes its effect felt within a higher-order term which depends on the perturber-core total cross section ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{tot}}^{\mathit{A}+\mathrm{\ensuremath{-}}}$B and the matrix element 〈${\mathit{r}}^{\mathrm{\ensuremath{-}}2}$〉nl{\mathrm{〉}}_{\mathit{n}\mathit{l}}〉nl​. The theoretical cross sections obtained for Cs and Rb atoms' J-mixing processes exhibit a similar dependence on the principal quantum number n as the experimental results, expecially in the lower-n states and for the heavier noble-gas atoms.