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Physical Review A

Photoassociation spectroscopy of Rb287(5s1∕2+5p1∕2)0u+ long-range molecular states: Coupling with the (5s1∕2+5p3∕2)0u+ series analyzed using the Lu-Fano approach

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

Published Jul 28, 2006• 22 citations
Publisher

Abstract

We report on photoassociation of cold $^{87}\mathrm{Rb}$ atoms providing the spectroscopy of $(5{s}_{1∕2}+5{p}_{1∕2}){0}_{u}^{+}$ 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 $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ 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 $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ levels, to evaluate the coupling, and to predict the energy and width of the first predissociated level of $(5{s}_{1∕2}+5{p}_{3∕2}){0}_{u}^{+}$ series. An experimental spectrum confirms the prediction.

DOI
10.1103/physreva.74.012510

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Spectroscopie photoassociative des états moléculaires à longue distance de 87Rb. Analyse Lu-Fano et amélioration de la formule de Le Roy-Bernstein

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

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 ).

Journal de Physique IV (Proceedings)•Oct 1, 2006•0 citations
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{-}12.5\ensuremath−12.5, \ensuremath−0.7cm\ensuremath−1\ensuremath{-}0.7\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\ensuremath−0.7cm\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.
We report on cold atom photoassociation of 87Rb^{87}\mathrm{Rb}87Rb 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.
We present an analysis of spectroscopic data concerning the long-range molecular state (6s1∕2+6p1∕2)0u+(6{s}_{1∕2}+6{p}_{1∕2}){0}_{u}^{+}(6s1∕2​+6p1∕2​)0u+​ of 133Cs2^{133}\mathrm{Cs}_{2}133Cs2​ [M. Pichler, H. Chen, and W. C. Stwalley, J. Chem. Phys. 121, 1796 (2004)] by using the Lu-Fano method coupled to the improved LeRoy-Bernstein formula. The obtained Lu-Fano graph exhibits the coupling of molecular series to the (6s1∕2+6p3∕2)0u+(6{s}_{1∕2}+6{p}_{3∕2}){0}_{u}^{+}(6s1∕2​+6p3∕2​)0u+​ state. The coupling is due to the spin effects in the molecule. A two-channel model involving the improved LeRoy-Bernstein formula allows us to characterize the molecular series, to localize the perturbing levels, to evaluate the coupling in the vicinity of each perturbing level (five observed for Cs) in a two-level approach and in a more accurate multilevel description. Furthermore, we predict the energy and the width of the first predissociated level.
Recently, the method of Lu-Fano plots was extended to potentials with general ${R}^{\ensuremath{-}n}$ asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrational spectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the Cs20u+(6S+6P1/2,3/2){\mathrm{Cs}}_{2}{0}_{u}^{+}{(6S+6P}_{1/2,3/2})Cs2​0u+​(6S+6P1/2,3/2​) photoassociation spectra below the 6S+P1/2{6S+P}_{1/2}6S+P1/2​ and 6S+P3/2{6S+P}_{3/2}6S+P3/2​ dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients C3{C}_{3}C3​ for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the 6S+P3/2{6S+P}_{3/2}6S+P3/2​ threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.
We demonstrate photoassociation (PA) of ultracold fermionic 87Sr^{87}\mathrm{Sr}87Sr atoms. The binding energies of a series of molecular states on the $^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}\phantom{\rule{4pt}{0ex}}5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}+5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ molecular potential are fit with the semiclassical LeRoy-Bernstein model, and PA resonance strengths are compared to predictions based on the known 1S0+1S0^{1}S_{0}+^{1}S_{0}1S0​+1S0​ ground-state potential. Similar measurements and analysis were performed for the bosonic isotopes 84Sr^{84}\mathrm{Sr}84Sr and 86Sr^{86}\mathrm{Sr}86Sr, allowing a combined analysis of the long-range portion of the excited-state potential and determination of the 5s5p1P15s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}5s5p1P1​ atomic state lifetime of $5.20\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. The results enable prediction of PA rates across a wide range of experimental conditions.
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 ).