Physical Review A

Photoassociation spectroscopy of {sup 87}Rb{sub 2} (5s{sub 1/2}+5p{sub 1/2})0{sub g}{sup -} long-range molecular states: Analysis by Lu-Fano graph and improved LeRoy-Bernstein formula

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

Published Mar 15, 2006• 0 citations

Abstract

We report on cold atom photoassociation of {sup 87}Rb giving spectroscopy data of the (5s{sub 1/2}+5p{sub 1/2})0{sub g}{sup -} long-range molecular states in the asymptotic range of [-12.5 cm{sup -1}, -1.5 cm{sup -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{sub g}{sup -} series.

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Physical Review A

Photoassociation spectroscopy of {sup 87}Rb{sub 2} (5s{sub 1/2}+5p{sub 1/2})0{sub g}{sup -} long-range molecular states: Analysis by Lu-Fano graph and improved LeRoy-Bernstein formula

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

Published Mar 15, 2006• 0 citations

OpenAlex

Abstract

Related papers

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

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.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.

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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

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Data on the $(5{s}_{1/2}+5{p}_{1/2}){1}_{g}$ ${}^{87}{\text{Rb}}_{2}$ state under the ${D}_{1}$ 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 ${c}_{6}$ 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 ${c}_{6}$ [${c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ a.u.].Data on the $(5{s}_{1/2}+5{p}_{1/2}){1}_{g}$ ${}^{87}{\text{Rb}}_{2}$ state under the ${D}_{1}$ 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 ${c}_{6}$ 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 ${c}_{6}$ [${c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ a.u.].

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Long range Rb{sub 2} excited state dispersion interactions and transition dipole moment from photoassociation spectra

M. Marinescu, A. Dalgarno, Chin‐Chun Tsai +3 more

Two identical alkali atoms, with one atom excited, interact at long range through the resonant dipole interaction - C{sub 3}/R{sup 3} and through the dispersion interaction - C{sub 6}/R{sup 6} - C{sub 8}/R{sup 8} - ... These interaction coefficients have been previously calculated, but not accurately measured. The authors have measured the bound levels of a unique, 0{sub g}{sup {minus}}{open_quotes} pure long range state{close_quotes} of {sub 87}Rb{sub 2} and {sup 85}Rb{sub 2} with photoassociation spectroscopy of ultracold Rb atoms. By fitting the levels predicted by the interaction Hamiltonian to the observed levels, they have derived accurate values of both C{sub 3} and of the dispersion interaction coefficients. They also obtain an accurate measurement of the Rb 5s-5p electric dipole matrix element, which is simply related to C{sub 3}. These results provide an excellent test of the theory. They are also important to cold collisions, which are very sensitive to long range interactions.Two identical alkali atoms, with one atom excited, interact at long range through the resonant dipole interaction - C{sub 3}/R{sup 3} and through the dispersion interaction - C{sub 6}/R{sup 6} - C{sub 8}/R{sup 8} - ... These interaction coefficients have been previously calculated, but not accurately measured. The authors have measured the bound levels of a unique, 0{sub g}{sup {minus}}{open_quotes} pure long range state{close_quotes} of {sub 87}Rb{sub 2} and {sup 85}Rb{sub 2} with photoassociation spectroscopy of ultracold Rb atoms. By fitting the levels predicted by the interaction Hamiltonian to the observed levels, they have derived accurate values of both C{sub 3} and of the dispersion interaction coefficients. They also obtain an accurate measurement of the Rb 5s-5p electric dipole matrix element, which is simply related to C{sub 3}. These results provide an excellent test of the theory. They are also important to cold collisions, which are very sensitive to long range interactions.

Bulletin of the American Physical SocietyMay 1, 19960 citations

Photoassociation spectroscopy of long range molecular states $\ ^{87}$ Rb. Lu-Fano analysis and improved Le Roy-BernsteinPhotoassociation spectroscopy of long range molecular states $\ ^{87}$Rb. Lu-Fano analysis and improved Le Roy-Bernstein

Haikel Jelassi, B. Viaris de Lesegno, Laurence Pruvost

Bulletin of the American Physical SocietyMay 17, 20060 citations

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.

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.

Data on the

(5{s}_{1/2}+5{p}_{1/2}){1}_{g}

{}^{87}{\text{Rb}}_{2}

state under the

{D}_{1}

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

{c}_{6}

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

{c}_{6}

[${c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}$ a.u.].

Photoassociation spectroscopy of long range molecular states

\ ^{87}

Rb. Lu-Fano analysis and improved Le Roy-Bernstein