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Physical Review A

Reexamination of the 0g− pure long-range state of Cs2 : Prediction of missing levels in the photoassociation spectrum

Nadia Bouloufa-Maafa, A. Crubellier, Olivier Dulieu

Published May 7, 2007• 45 citations
Publisher

Abstract

A reexamination of the photoassociation spectrum of the external well of the ${0}_{g}^{\ensuremath{-}}$ potential of ${\mathrm{Cs}}_{2}$ converging to the $(6{s}_{1∕2}+6{p}_{3∕2})$ limit is performed, in order to resolve inconsistencies arising from a previously published paper [Phys. Rev. Lett. 85, 1408 (2000)]. We use the same analytical description of the potential as in an other previous analysis [Phys. Rev. A 66, 052506 (2002)], but we make a shift of 2 in the assignment of the observed vibrational lines. The agreement between experimental and calculated energy positions is improved and the intensities calculated using the new potential account well for all available data. The fitting procedure reveals a strong interdependence of the parameters of the model, which limits the accuracy of the determination of the radiative lifetimes of the $6{p}^{2}{P}_{1∕2}$ and $6{p}^{2}{P}_{3∕2}$ atomic levels. Only a more precise experimental study could allow one to improve the determination of these lifetime values.

DOI
10.1103/physreva.75.052501

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A reexamination of the photoassociation spectrum of the external well of the 0g\ensuremath−{0}_{g}^{\ensuremath{-}}0g\ensuremath−​ potential of Cs2{\mathrm{Cs}}_{2}Cs2​ converging to the (6s1∕2+6p3∕2)(6{s}_{1∕2}+6{p}_{3∕2})(6s1∕2​+6p3∕2​) limit is performed, in order to resolve inconsistencies arising from a previously published paper [Phys. Rev. Lett. 85, 1408 (2000)]. We use the same analytical description of the potential as in an other previous analysis [Phys. Rev. A 66, 052506 (2002)], but we make a shift of 2 in the assignment of the observed vibrational lines. The agreement between experimental and calculated energy positions is improved and the intensities calculated using the new potential account well for all available data. The fitting procedure reveals a strong interdependence of the parameters of the model, which limits the accuracy of the determination of the radiative lifetimes of the 6p2P1∕26{p}^{2}{P}_{1∕2}6p2P1∕2​ and 6p2P3∕26{p}^{2}{P}_{3∕2}6p2P3∕2​ atomic levels. Only a more precise experimental study could allow one to improve the determination of these lifetime values.
An analytical expression for the external well of the ${\mathrm{Cs}}_{2}{0}_{g}^{\ensuremath{-}}{(6s+6P}_{3/2})$ double-well potential curve is derived, involving asymptotic parameters fitted on the spectrum obtained from photoassociation of ultracold cesium atoms and ultracold molecule formation [Fioretti et al., Europhys. J. D 5, 389 (1999)]. The results are compared to a previous Rydberg-Klein-Rees determination from our group, and may have consequences on the determination of cesium triplet scattering length. Values for radiative lifetimes ${\ensuremath{\tau}}_{3/2}=30.462(3)$ ns and ${\ensuremath{\tau}}_{1/2}=34.88(2)$ ns of the 6P3/2{6P}_{3/2}6P3/2​ and 6P1/2{6P}_{1/2}6P1/2​ atomic levels, respectively, are extracted with an accuracy better than previous determinations. The method of Derevianko and Porsev [Phys. Rev. A 65, 053403 (2002)], allows the derivation of an improved value for the van der Waals coefficient of ground-state cesium molecule, C66s=6828(19){C}_{6}^{6s}=6828(19)C66s​=6828(19) a.u.
We have experimentally observed the two lowest vibrational levels of Cs2{}_{2}2​ 0${}_{g}^{\ensuremath{-}}$ purely-long-range states. The photoassociation spectroscopy of ultracold cesium atoms with rotational structure presents clear identification of these lowest levels. Values of radiative lifetimes ${\ensuremath{\tau}}_{3/2}=30.41\ifmmode\pm\else\textpm\fi{}0.06$ ns and ${\ensuremath{\tau}}_{1/2}=34.81\ifmmode\pm\else\textpm\fi{}0.07$ ns of the 6p2P1/2p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}p2P1/2​and 6p2P3/2p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}\phantom{\rule{0.28em}{0ex}}p2P3/2​atomic levels and van der Waals coefficient ${C}_{6}=6852\ifmmode\pm\else\textpm\fi{}25$ a.u. of the ground-state cesium molecule are extracted, respectively.
High-resolution photoassociation spectroscopy is reported using a modulation spectroscopy technology in a cesium atomic magneto-optical trap. The two lowest vibrational levels have been experimentally observed which have been theo- retically predicted in [Phys. Rev. A 75 052501 （2007）]. A new potential curve is obtained by using the Rydberg-Klein-Ress method with a well depth of -82,384 ＋ 0,026 cm-1, which is deeper than the result of previous experiment （-77.909 cm-1） and the theoretical prediction （-81.6445 cm- l ）.
Spectroscopy of the high-lying vibrational levels of the 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ and 1sp1Sigmasbspu+1\\sp1\\Sigma\\sbsp{u}{+}1sp1Sigmasbspu+ states of both rmsp6Lisb2\\rm\\sp6Li\\sb2rmsp6Lisb2 and rmsp7Lisb2\\rm\\sp7Li\\sb2rmsp7Lisb2 has been accomplished via photoassociation of ultracold atomic lithium confined in a magneto-optical trap. Both these molecular states correlate to 2Ssb1/22S\\sb{1/2}2Ssb1/2 plus 2Psb1/22P\\sb{1/2}2Psb1/2 free atomic states. The long range part of these molecular potentials depends on the 2P atomic radiative lifetime. Accurate models were constructed for both the 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ and 1sp1Sigmasbspu+1\\sp1\\Sigma\\sbsp{u}{+}1sp1Sigmasbspu+ potentials. By fitting these models to the experimentally measured vibrational levels observed in rmsp6Lisb2\\rm\\sp6Li\\sb2rmsp6Lisb2 and rmsp7Lisb2\\rm\\sp7Li\\sb2rmsp7Lisb2, we have been able to extract a value for the 2P lifetime of lithium. Fitting to the absolute values of the data gives a value of 26.99 pm\\pmpm 0.16 ns whereas fitting to differences in the spectral features gives a value of 27.04 pm\\pmpm 0.18 ns. While both values agree with previous work, improvements made in the potential models would enable this analysis to resolve the current discrepancy between experiment and theory.
The photoassociation spectroscopic data of the long-range molecular 1g state of Cs 2 in the asymptotic range red detuned [-5.02, -2.45 cm -1 ] to the (6S 1/2 +6P 3/2 ) dissociation limit detected using photon counting technique are presented and 18 new high-lying vibrational energy levels are obtained. Fitting experimental data to the improved LeRoy–Bernstein (LRB) formula, we have obtained the long-range molecular coefficient c 3 with a high precision and also demonstrated the necessity of the improved LRB formula for more precise c 3 coefficient by analyzing the residual from fitting procedure.