Physical Review A

Determination of the 87Rb 5p state dipole matrix element and radiative lifetime from the photoassociation spectroscopy of the Rb2 0g−(P3/2) long-range state

Ricardo Fraga Gutterres, Claude Amiot, A. Fioretti, C. Gabbanini, Marina Mazzoni, Olivier Dulieu

Published Aug 14, 2002• 77 citations

Abstract

We present a detailed study of the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ pure long-range electronic state of the ${}^{87}{\mathrm{Rb}}_{2}$ molecule. The high-resolution spectral data provided by photoassociative spectroscopy of ${}^{87}{\mathrm{Rb}}_{2}$ is analyzed by using the generalized simulated annealing method. The dipole matrix element of the $5p$ ${}^{87}\mathrm{Rb}$ atomic state and other effective asymptotic parameters for the ${0}_{g}^{\ensuremath{-}}{(P}_{3/2})$ long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the ${5P}_{3/2}$ and ${5P}_{1/2}$ states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.

DOI: 10.1103/physreva.66.024502

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

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Physical Review A

Determination of the 87Rb 5p state dipole matrix element and radiative lifetime from the photoassociation spectroscopy of the Rb2 0g−(P3/2) long-range state

Ricardo Fraga Gutterres, Claude Amiot, A. Fioretti, C. Gabbanini, Marina Mazzoni, Olivier Dulieu

Published Aug 14, 2002• 77 citations

Publisher

Abstract

We present a detailed study of the

{0}_{g}^{\ensuremath{-}}{(P}_{3/2})

pure long-range electronic state of the

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

molecule. The high-resolution spectral data provided by photoassociative spectroscopy of

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

is analyzed by using the generalized simulated annealing method. The dipole matrix element of the

5p

{}^{87}\mathrm{Rb}

atomic state and other effective asymptotic parameters for the

{0}_{g}^{\ensuremath{-}}{(P}_{3/2})

long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the

{5P}_{3/2}

and

{5P}_{1/2}

states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.

DOI: 10.1103/physreva.66.024502

Related papers

Precise determination of the dipole matrix element and radiative lifetime of the K39 4p state by photoassociative spectroscopy

H. Wang, J. Li, X. T. Wang +3 more

Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of $^{39}\mathrm{K}_{2}$ are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ ${\mathrm{nm}}^{3}$ (-8.445(14) a.u.), \ensuremath{\tau}(4 ${\mathrm{}}^{2}$ ${\mathrm{P}}_{3\mathrm{/}2}$ )=26.34(5) ns, and \ensuremath{\tau}(4 ${\mathrm{}}^{2}$ ${\mathrm{P}}_{1\mathrm{/}2}$ )=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of $^{39}\mathrm{K}_{2}$ are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ ${\mathrm{nm}}^{3}$ (-8.445(14) a.u.), \ensuremath{\tau}(4${\mathrm{}}^{2}$${\mathrm{P}}_{3\mathrm{/}2}$)=26.34(5) ns, and \ensuremath{\tau}(4${\mathrm{}}^{2}$${\mathrm{P}}_{1\mathrm{/}2}$)=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].

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Precise determination of the 2P radiative atomic lifetime of lithium using photoassociative spectroscopy

W. I. McAlexander

Spectroscopy of the high-lying vibrational levels of the $1\\sp3\\Sigma\\sbsp{g}{+}$ and $1\\sp1\\Sigma\\sbsp{u}{+}$ states of both $\\rm\\sp6Li\\sb2$ and $\\rm\\sp7Li\\sb2$ has been accomplished via photoassociation of ultracold atomic lithium confined in a magneto-optical trap. Both these molecular states correlate to $2S\\sb{1/2}$ plus $2P\\sb{1/2}$ 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 $1\\sp3\\Sigma\\sbsp{g}{+}$ and $1\\sp1\\Sigma\\sbsp{u}{+}$ potentials. By fitting these models to the experimentally measured vibrational levels observed in $\\rm\\sp6Li\\sb2$ and $\\rm\\sp7Li\\sb2$ , 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 $\\pm$ 0.16 ns whereas fitting to differences in the spectral features gives a value of 27.04 $\\pm$ 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.Spectroscopy of the high-lying vibrational levels of the $1\\sp3\\Sigma\\sbsp{g}{+}$ and $1\\sp1\\Sigma\\sbsp{u}{+}$ states of both $\\rm\\sp6Li\\sb2$ and $\\rm\\sp7Li\\sb2$ has been accomplished via photoassociation of ultracold atomic lithium confined in a magneto-optical trap. Both these molecular states correlate to $2S\\sb{1/2}$ plus $2P\\sb{1/2}$ 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 $1\\sp3\\Sigma\\sbsp{g}{+}$ and $1\\sp1\\Sigma\\sbsp{u}{+}$ potentials. By fitting these models to the experimentally measured vibrational levels observed in $\\rm\\sp6Li\\sb2$ and $\\rm\\sp7Li\\sb2$, 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 $\\pm$ 0.16 ns whereas fitting to differences in the spectral features gives a value of 27.04 $\\pm$ 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.

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Journal of Physics B Atomic Molecular and Optical PhysicsSep 25, 200653 citations

Determination of the Cs20g−(P3/2) potential curve and of Cs6P1/2,3/2 atomic radiative lifetimes from photoassociation spectroscopy

Claude Amiot, Olivier Dulieu, Ricardo Fraga Gutterres +1 more

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 ${6P}_{3/2}$ and ${6P}_{1/2}$ 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, ${C}_{6}^{6s}=6828(19)$ a.u.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 ${6P}_{3/2}$ and ${6P}_{1/2}$ 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, ${C}_{6}^{6s}=6828(19)$ a.u.

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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

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.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.

Physical Review AMay 7, 200745 citations

Precise atomic radiative lifetime via photoassociative spectroscopy of ultracold lithium

W. I. McAlexander, E. R. I. Abraham, Nicholas W. M. Ritchie +3 more

We have obtained spectra of the high-lying vibrational levels of the ${1}^{3}$ ${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of $^{6}\mathrm{Li}_{2}$ via photoassociation of ultracold $^{6}\mathrm{Li}$ atoms confined in a magneto-optical trap. The ${1}^{3}$ ${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of the diatomic molecule correlates to a 2 ${\mathit{S}}_{1/2}$ state atom plus a 2 ${\mathit{P}}_{1/2}$ state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the ${1}^{3}$ ${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99\ifmmode\pm\else\textpm\fi{}0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.We have obtained spectra of the high-lying vibrational levels of the ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of $^{6}\mathrm{Li}_{2}$ via photoassociation of ultracold $^{6}\mathrm{Li}$ atoms confined in a magneto-optical trap. The ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of the diatomic molecule correlates to a 2${\mathit{S}}_{1/2}$ state atom plus a 2${\mathit{P}}_{1/2}$ state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the ${1}^{3}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99\ifmmode\pm\else\textpm\fi{}0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.

Physical Review AFeb 1, 1995123 citations

We present a detailed study of the

{0}_{g}^{\ensuremath{-}}{(P}_{3/2})

pure long-range electronic state of the

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

molecule. The high-resolution spectral data provided by photoassociative spectroscopy of

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

is analyzed by using the generalized simulated annealing method. The dipole matrix element of the

5p

{}^{87}\mathrm{Rb}

atomic state and other effective asymptotic parameters for the

{0}_{g}^{\ensuremath{-}}{(P}_{3/2})

long-range state are determined and a complete analytical description of the potential well is obtained. We extract a radiative lifetime of the

{5P}_{3/2}

and

{5P}_{1/2}

states equal to 26.25(8) ns and 27.75(8) ns, respectively, with a precision (0.3%) comparable to atomic physics experiment.

Rovibrational levels (v=0--30) of the ${0}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ ``pure long-range'' state of

^{39}\mathrm{K}_{2}

are observed by photoassociative spectroscopy of ultracold potassium atoms prepared in a high-density magneto-optical trap. The measured molecular binding energies are used to precisely determine the long-range dipole-dipole potential constant ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$ of the K(4s)+K(4p) asymptote and the radiative lifetime of the 4p state. We determine ${\mathrm{C}}_{3}^{\mathrm{\ensuremath{\Pi}}}$=-5.456(9) zJ

{\mathrm{nm}}^{3}

(-8.445(14) a.u.), \ensuremath{\tau}(4

{\mathrm{}}^{2}

{\mathrm{P}}_{3\mathrm{/}2}

)=26.34(5) ns, and \ensuremath{\tau}(4

{\mathrm{}}^{2}

{\mathrm{P}}_{1\mathrm{/}2}

)=26.69(5) ns. Our result is a significant improvement in precision over previous lifetime measurements and agrees well with the recent fast-beam experiment [U. Volz and H. Schmoranzer, Phys. Scr. T65, 48 (1996)].

Spectroscopy of the high-lying vibrational levels of the

1\\sp3\\Sigma\\sbsp{g}{+}

and

1\\sp1\\Sigma\\sbsp{u}{+}

states of both

\\rm\\sp6Li\\sb2

and

\\rm\\sp7Li\\sb2

has been accomplished via photoassociation of ultracold atomic lithium confined in a magneto-optical trap. Both these molecular states correlate to

2S\\sb{1/2}

plus

2P\\sb{1/2}

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

1\\sp3\\Sigma\\sbsp{g}{+}

and

1\\sp1\\Sigma\\sbsp{u}{+}

potentials. By fitting these models to the experimentally measured vibrational levels observed in

\\rm\\sp6Li\\sb2

and

\\rm\\sp7Li\\sb2

, 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

0.16 ns whereas fitting to differences in the spectral features gives a value of 27.04

\\pm

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.

{6P}_{3/2}

and

{6P}_{1/2}

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,

{C}_{6}^{6s}=6828(19)

a.u.

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.

We have obtained spectra of the high-lying vibrational levels of the

{1}^{3}

${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of

^{6}\mathrm{Li}_{2}

via photoassociation of ultracold

^{6}\mathrm{Li}

atoms confined in a magneto-optical trap. The

{1}^{3}

${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state of the diatomic molecule correlates to a 2

{\mathit{S}}_{1/2}

state atom plus a 2

{\mathit{P}}_{1/2}

state atom. The long-range part of the molecular interaction potential for this state depends on the 2P atomic radiative lifetime. By calculating the energy eigenvalues of a model potential for the

{1}^{3}

${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ state and fitting them to the experimentally measured vibrational levels, we have extracted a value for the 2P lifetime of 26.99\ifmmode\pm\else\textpm\fi{}0.16 ns. The precision is currently limited by the accuracy of a region of the model potential provided by ab initio calculations.