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Physical Review A

Photoassociation spectroscopy of Rb287 (5s1∕2+5p1∕2)0g− long-range molecular states: Analysis by Lu-Fano graph and improved LeRoy-Bernstein formula

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

Published Mar 2, 2006• 35 citations
Publisher

Abstract

We report on cold atom photoassociation of $^{87}\mathrm{Rb}$ giving spectroscopy data of the $(5{s}_{1∕2}+5{p}_{1∕2}){0}_{g}^{\ensuremath{-}}$ long-range molecular states in the asymptotic range of [$\ensuremath{-}12.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, $\ensuremath{-}1.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the ${0}_{g}^{\ensuremath{-}}$ series.

DOI
10.1103/physreva.73.032501

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中国物理B：英文版•Jan 1, 2013•0 citations
We report on cold atom photoassociation of 87Rb^{87}\mathrm{Rb}87Rb giving spectroscopy data of the (5s1∕2+5p1∕2)0g\ensuremath−(5{s}_{1∕2}+5{p}_{1∕2}){0}_{g}^{\ensuremath{-}}(5s1∕2​+5p1∕2​)0g\ensuremath−​ long-range molecular states in the asymptotic range of [\ensuremath−12.5cm\ensuremath−1\ensuremath{-}12.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\ensuremath−12.5cm\ensuremath−1, \ensuremath−1.5cm\ensuremath−1\ensuremath{-}1.5\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\ensuremath−1.5cm\ensuremath−1] below the dissociation limit. Using a Lu-Fano approach to analyze the data, we show that an improved LeRoy-Bernstein model has to be applied. This approach lets us determine the phase shift of the wave function at the dissociation limit of the 0g\ensuremath−{0}_{g}^{\ensuremath{-}}0g\ensuremath−​ series.
We report on photoassociation of cold 87Rb^{87}\mathrm{Rb}87Rb atoms providing the spectroscopy of (5s1∕2+5p1∕2)0u+(5{s}_{1∕2}+5{p}_{1∕2}){0}_{u}^{+}(5s1∕2​+5p1∕2​)0u+​ long-range molecular states, in the energy range of [$\ensuremath{-}12.5$, $\ensuremath{-}0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$] below the dissociation limit. A Lu-Fano approach coupled to the LeRoy-Bernstein formula is used to analyze the data. The Lu-Fano graph exhibits the coupling of the molecular series with the (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ one, which is due to spin effects in the molecule. A two-channel model involving an improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ levels, to evaluate the coupling, and to predict the energy and width of the first predissociated level of (5s1∕2+5p3∕2)0u+(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}(5s1∕2​+5p3∕2​)0u+​ series. An experimental spectrum confirms the prediction.
Data on the (5s1/2+5p1/2)1g(5{s}_{1/2}+5{p}_{1/2}){1}_{g}(5s1/2​+5p1/2​)1g​ 87Rb2{}^{87}{\text{Rb}}_{2}87Rb2​ state under the D1{D}_{1}D1​ limit, provided by a photoassociation experiment on cold atoms, have been analyzed by an improved LeRoy-Bernstein (LRB) approach including linear and nonlinear terms and provide a c6{c}_{6}c6​ value of the potential. To do that, using a model for hyperfine structure shifts, we have first subtracted the hyperfine effects in the split lines and deduced the vibrational energies. Then, we have compared three LRB-type models to fit the data. We conclude that the second-order improved LRB is well suited and allows us to deduce an experimental value of c6{c}_{6}c6​ [${c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ a.u.].
Photoassociation spectroscopy of long range molecular states  87\ ^{87} 87Rb. Lu-Fano analysis and improved Le Roy-Bernstein
Nous avons etudie la photoassociation de 87 Rb sous la limite 5S 1/2 + 5P 1/2 (D 1 ), par spectroscopie de pertes d'atomes froids. Les spectres montrent les progressions vibrationnelles des trois series d'etats moleculaires attractifs 0 - g , 0 + u et l g convergents vers la limite 5S 1/2 +5P 1/2 . L'analyse de nos donnees utilise l'approche de Lu-Fano associe au modele de LeRoy-Bernstein. Pour la serie 0 - g , cette approche met en evidence un ecart au modele. Une amelioration de la formule de LeRoy-Bernstein permet de rendre compte des mesures experimentales. Pour la serie 0 + u (P 1/2 ) avec la meme methode, on montre le couplage avec la serie 0 + u (P 3/2 ).