Physical Review A

Weakly bound 87 Rb 2 (5s1/2+5p1/2)1g molecules: Hyperfine interaction and LeRoy-Bernstein analysis including linear and nonlinear terms

Haikel Jelassi, Laurence Pruvost

Published Mar 20, 2014• 10 citations

Abstract

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.].

DOI: 10.1103/physreva.89.032514

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

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Physical Review AMar 2, 200635 citations

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

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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Weakly bound (6s1/2+ 6p1/2)0−gCs2levels analysed using the vibrational quantum defect: detection of two deeply bound (6s1/2+ 6p3/2)0−glevels

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Physical Review AFeb 26, 200437 citations

Physical Review A

Weakly bound 87 Rb 2 (5s1/2+5p1/2)1g molecules: Hyperfine interaction and LeRoy-Bernstein analysis including linear and nonlinear terms

Haikel Jelassi, Laurence Pruvost

Published Mar 20, 2014• 10 citations

Publisher

Abstract

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.].

DOI: 10.1103/physreva.89.032514

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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.

Physical Review AMar 2, 200635 citations

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

Physical Review AMar 15, 20060 citations

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

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.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.

Physical Review AJul 28, 200622 citations

Hyperfine and vibrational structure of weakly bound levels of the lowest 1g state of molecular 87 Rb 2

Chin‐Chun Tsai, T. H. Bergeman, Eite Tiesinga +2 more

Photoassociation resonances in the ${}^{87}$ Rb ${}_{2}$ ${1}_{g}$ state dissociating to $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ were produced by the excitation of colliding ${}^{87}$ Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin $I=3$ were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters $A(v)$ , vibrational $G(v)$ , and rotational $B(v)$ parameters. The $G(v)$ parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current ${C}_{3}$ and ${C}_{6}$ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.Photoassociation resonances in the ${}^{87}$Rb${}_{2}$ ${1}_{g}$ state dissociating to $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ were produced by the excitation of colliding ${}^{87}$Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the $5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}$ limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin $I=3$ were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters $A(v)$, vibrational $G(v)$, and rotational $B(v)$ parameters. The $G(v)$ parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current ${C}_{3}$ and ${C}_{6}$ long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.

Physical Review ANov 13, 20134 citations

Weakly bound (6s1/2+ 6p1/2)0−gCs2levels analysed using the vibrational quantum defect: detection of two deeply bound (6s1/2+ 6p3/2)0−glevels

Laurence Pruvost, Haikel Jelassi

1 Weakly bound (6s 1/2 +6p 1/2)0 g - Cs 2 levels analysed using the vibrational quantum defect. Detection of two deeply bound (6s 1/2 +6p 3/2)0 g - levels. Abstract. We report on the analysis of the (6s 1/2 +6p 1/2)0 g - weakly-bound levels of Cs 2 detected by photoassociation spectroscopy. We compare three methods of analysis: the use of the LeRoy-Bernstein formula, the use of the improved LeRoy-Bernstein formula and the use of the vibrational quantum defect. We show that the vibrational quantum defect method is more sensitive than the other methods and allows us to detect two deeplybound levels of the (6s 1/2 +6p 3/2)0 g - potential, which are not detected by the others methods. The binding energies of the levels are found to be 565.49 cm -1 and 591.43 cm-1 below the (6s 1/2 +6p 3/2) dissociation limit.1 Weakly bound (6s 1/2 +6p 1/2)0 g - Cs 2 levels analysed using the vibrational quantum defect. Detection of two deeply bound (6s 1/2 +6p 3/2)0 g - levels. Abstract. We report on the analysis of the (6s 1/2 +6p 1/2)0 g - weakly-bound levels of Cs 2 detected by photoassociation spectroscopy. We compare three methods of analysis: the use of the LeRoy-Bernstein formula, the use of the improved LeRoy-Bernstein formula and the use of the vibrational quantum defect. We show that the vibrational quantum defect method is more sensitive than the other methods and allows us to detect two deeplybound levels of the (6s 1/2 +6p 3/2)0 g - potential, which are not detected by the others methods. The binding energies of the levels are found to be 565.49 cm -1 and 591.43 cm-1 below the (6s 1/2 +6p 3/2) dissociation limit.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 1, 201011 citations

Near-threshold photoassociation of 87Rb2

M. Kemmann, Ivan Mistrík, S. Nußmann +3 more

Photoassociation of cold ${}^{87}\mathrm{Rb}{(5s,f}_{b}=2)$ atom pairs is studied within 13 GHz of the dissociation limits ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{)+}^{87}\mathrm{Rb}{(5s,f}_{b}=2).$ Vibrational levels in the long range, hyperfine manifolds of the ${0}_{g}^{\ensuremath{-}}$ and ${1}_{g}$ states arising from the ${}^{87}\mathrm{Rb}{(5p}_{3/2})$ fine structure limit are identified to lead to the formation of stable molecules in the photoassociation process. The vibrational bands are observed to break off, at positions matching the energetic location of potential-energy barriers predicted in the hyperfine manifolds at about 1 GHz above the ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{=3)+}^{87}\mathrm{Rb}{(5s,f}_{b}=1)$ dissociation limit. Empiricial potential-energy curves are derived from the data. These are found to be in agreement with predictions based on the long-range hyperfine recoupling of the excited molecular states. The selectivity of the excitation process and predissociation mechanisms are discussed.Photoassociation of cold ${}^{87}\mathrm{Rb}{(5s,f}_{b}=2)$ atom pairs is studied within 13 GHz of the dissociation limits ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{)+}^{87}\mathrm{Rb}{(5s,f}_{b}=2).$ Vibrational levels in the long range, hyperfine manifolds of the ${0}_{g}^{\ensuremath{-}}$ and ${1}_{g}$ states arising from the ${}^{87}\mathrm{Rb}{(5p}_{3/2})$ fine structure limit are identified to lead to the formation of stable molecules in the photoassociation process. The vibrational bands are observed to break off, at positions matching the energetic location of potential-energy barriers predicted in the hyperfine manifolds at about 1 GHz above the ${}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{=3)+}^{87}\mathrm{Rb}{(5s,f}_{b}=1)$ dissociation limit. Empiricial potential-energy curves are derived from the data. These are found to be in agreement with predictions based on the long-range hyperfine recoupling of the excited molecular states. The selectivity of the excitation process and predissociation mechanisms are discussed.

Physical Review AFeb 26, 200437 citations

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}

{c}_{6}

[

{c}_{6}=(15.14\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{4}

a.u.].

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.

Photoassociation resonances in the

{}^{87}

{}_{2}

{1}_{g}

state dissociating to

5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}

were produced by the excitation of colliding

{}^{87}

Rb atoms in a far-off resonance trap. Levels down to 31 cm${}^{\ensuremath{-}1}$ below the dissociation limit were measured with resonance linewidths of 15 to 20 MHz, and have been located to a one-sigma combined systematic and statistical uncertainty of 50 MHz relative to the

5{\phantom{\rule{0.16em}{0ex}}}^{2}S+5{}^{2}{P}_{1/2}

limit. Electron and nuclear spins were fixed to a space-fixed axis by circularly polarized optical pumping, so that only states with total nuclear spin

I=3

were excited, thereby greatly simplifying the spectrum. The analysis of the data yielded hyperfine coupling parameters

A(v)

, vibrational

G(v)

, and rotational

B(v)

parameters. The

G(v)

parameters could be fit to an rms accuracy of about 0.01 cm${}^{\ensuremath{-}1}$ to a potential constructed from current

{C}_{3}

and

{C}_{6}

long-range dispersion parameters plus an ab initio potential that was adjusted in depth and with quadratic terms in the internuclear distance added to the inner wall.

Photoassociation of cold

{}^{87}\mathrm{Rb}{(5s,f}_{b}=2)

atom pairs is studied within 13 GHz of the dissociation limits

{}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{)+}^{87}\mathrm{Rb}{(5s,f}_{b}=2).

Vibrational levels in the long range, hyperfine manifolds of the ${0}_{g}^{\ensuremath{-}}$ and

{1}_{g}

states arising from the

{}^{87}\mathrm{Rb}{(5p}_{3/2})

fine structure limit are identified to lead to the formation of stable molecules in the photoassociation process. The vibrational bands are observed to break off, at positions matching the energetic location of potential-energy barriers predicted in the hyperfine manifolds at about 1 GHz above the

{}^{87}\mathrm{Rb}{(5p}_{3/2}{,f}_{a}{=3)+}^{87}\mathrm{Rb}{(5s,f}_{b}=1)

dissociation limit. Empiricial potential-energy curves are derived from the data. These are found to be in agreement with predictions based on the long-range hyperfine recoupling of the excited molecular states. The selectivity of the excitation process and predissociation mechanisms are discussed.