arXiv:2011.11936 · Physical Review A

Photoassociative spectroscopy of Sr87

Joshua C. Hill, William Huie, P. Lunia, J. D. Whalen, S. K. Kanungo, Y. Lu, T. C. Killian

Published Feb 17, 2021• 1 citation

Abstract

We demonstrate photoassociation (PA) of ultracold fermionic $^{87}\mathrm{Sr}$ 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 $^{1}S_{0}+^{1}S_{0}$ ground-state potential. Similar measurements and analysis were performed for the bosonic isotopes $^{84}\mathrm{Sr}$ and $^{86}\mathrm{Sr}$, allowing a combined analysis of the long-range portion of the excited-state potential and determination of the $5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}$ 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.

DOI: 10.1103/physreva.103.023111

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Photoassociation spectroscopy of Sr88 : Reconstruction of the wave function near the last node

Masami Yasuda, T. Kishimoto, Masao Takamoto +1 more

Physical Review AJan 27, 200673 citations

Mass scaling and nonadiabatic effects in photoassociation spectroscopy of ultracold strontium atoms

Mateusz Borkowski, Piotr Morzyński, R. Ciuryło +4 more

arXiv:1406.4365Physical Review ASep 16, 201440 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

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Analysis of photoassociation spectra for giant helium dimers

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Wave-Function Reconstruction for the Determination of the Scattering Length of Sr

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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

arXiv:2011.11936 · Physical Review A

Photoassociative spectroscopy of Sr87

Joshua C. Hill, William Huie, P. Lunia, J. D. Whalen, S. K. Kanungo, Y. Lu, T. C. Killian

Published Feb 17, 2021• 1 citation

arXiv HTML PDF

Abstract

We demonstrate photoassociation (PA) of ultracold fermionic

^{87}\mathrm{Sr}

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

^{1}S_{0}+^{1}S_{0}

ground-state potential. Similar measurements and analysis were performed for the bosonic isotopes

^{84}\mathrm{Sr}

and

^{86}\mathrm{Sr}

, allowing a combined analysis of the long-range portion of the excited-state potential and determination of the

5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}

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.

DOI: 10.1103/physreva.103.023111

Related papers

Photoassociation spectroscopy of Sr88 : Reconstruction of the wave function near the last node

Masami Yasuda, T. Kishimoto, Masao Takamoto +1 more

We have investigated photoassociation (PA) spectra of ultracold $^{88}\mathrm{Sr}$ atoms near the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}+5s5p\phantom{\rule{0.2em}{0ex}}^{1}P_{1}$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be ${r}_{0}=3.78(18)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ . The PA lines also determined a precise lifetime of the $^{1}P_{1}$ state to be $5.263(4)\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ .We have investigated photoassociation (PA) spectra of ultracold $^{88}\mathrm{Sr}$ atoms near the $5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}+5s5p\phantom{\rule{0.2em}{0ex}}^{1}P_{1}$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be ${r}_{0}=3.78(18)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The PA lines also determined a precise lifetime of the $^{1}P_{1}$ state to be $5.263(4)\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.

Physical Review AJan 27, 200673 citations

Mass scaling and nonadiabatic effects in photoassociation spectroscopy of ultracold strontium atoms

Mateusz Borkowski, Piotr Morzyński, R. Ciuryło +4 more

We report photoassociation spectroscopy of ultracold $^{86}\mathrm{Sr}$ atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date: $^{84}\mathrm{Sr},^{86}\mathrm{Sr}$ , and $^{88}\mathrm{Sr}$ . We attribute that to the recently discovered avoided crossing between the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ ${0}_{u}^{+}$ $({}^{3}{\ensuremath{\Pi}}_{u})$ and ${}^{1}{S}_{0}+{}^{1}{D}_{2}$ ${0}_{u}^{+}$ $({}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available ${0}_{u}^{+}$ and ${1}_{u}$ bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the ${0}_{u}^{+}$ and ${1}_{u}$ curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two $\ensuremath{-}8$-GHz bound states in $^{88}\mathrm{Sr}$ over the previously used model potentials. We show that one of the recently reported energy levels in $^{84}\mathrm{Sr}$ does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients ${C}_{6}({0}_{u}^{+})=3868(50)$ a.u. and ${C}_{6}({1}_{u})=4085(50)$ a.u. are reported.We report photoassociation spectroscopy of ultracold $^{86}\mathrm{Sr}$ atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date: $^{84}\mathrm{Sr},^{86}\mathrm{Sr}$, and $^{88}\mathrm{Sr}$. We attribute that to the recently discovered avoided crossing between the ${}^{1}{S}_{0}+{}^{3}{P}_{1}$ ${0}_{u}^{+}$ $({}^{3}{\ensuremath{\Pi}}_{u})$ and ${}^{1}{S}_{0}+{}^{1}{D}_{2}$ ${0}_{u}^{+}$ $({}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available ${0}_{u}^{+}$ and ${1}_{u}$ bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the ${0}_{u}^{+}$ and ${1}_{u}$ curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two $\ensuremath{-}8$-GHz bound states in $^{88}\mathrm{Sr}$ over the previously used model potentials. We show that one of the recently reported energy levels in $^{84}\mathrm{Sr}$ does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients ${C}_{6}({0}_{u}^{+})=3868(50)$ a.u. and ${C}_{6}({1}_{u})=4085(50)$ a.u. are reported.

arXiv:1406.4365Physical Review ASep 16, 201440 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

Analysis of photoassociation spectra for giant helium dimers

Jérémie Léonard, Allard P. Mosk, M. Walhout +3 more

We perform a theoretical analysis to interpret the spectra of purely long-range helium dimers produced by photoassociation (PA) in an ultracold gas of metastable helium atoms. The experimental spectrum obtained with the PA laser tuned closed to the $2\phantom{\rule{0.3em}{0ex}}^{3}S_{1}\ensuremath{\leftrightarrow}2\phantom{\rule{0.3em}{0ex}}^{3}P_{0}$ atomic line has been reported in a previous paper. Here, we first focus on the corrections to be applied to the measured resonance frequencies in order to infer the molecular binding energies. We then present a calculation of the vibrational spectra for the purely long-range molecular states, using adiabatic potentials obtained from perturbation theory. With retardation effects taken into account, the agreement between experimental and theoretical determinations of the spectrum for the ${0}_{u}^{+}$ purely long-range potential well is very good. The results yield a determination of the lifetime of the $2\phantom{\rule{0.3em}{0ex}}^{3}P$ atomic state.We perform a theoretical analysis to interpret the spectra of purely long-range helium dimers produced by photoassociation (PA) in an ultracold gas of metastable helium atoms. The experimental spectrum obtained with the PA laser tuned closed to the $2\phantom{\rule{0.3em}{0ex}}^{3}S_{1}\ensuremath{\leftrightarrow}2\phantom{\rule{0.3em}{0ex}}^{3}P_{0}$ atomic line has been reported in a previous paper. Here, we first focus on the corrections to be applied to the measured resonance frequencies in order to infer the molecular binding energies. We then present a calculation of the vibrational spectra for the purely long-range molecular states, using adiabatic potentials obtained from perturbation theory. With retardation effects taken into account, the agreement between experimental and theoretical determinations of the spectrum for the ${0}_{u}^{+}$ purely long-range potential well is very good. The results yield a determination of the lifetime of the $2\phantom{\rule{0.3em}{0ex}}^{3}P$ atomic state.

arXiv:quant-ph/0310006Physical Review AMar 5, 200427 citations

Wave-Function Reconstruction for the Determination of the Scattering Length of Sr

Masami Yasuda, T. Kishimoto, Masao Takamoto +1 more

We have investigated the photoassociation (PA) spectra of ultracold $^{88}$ Sr atoms near the $5s^2 ^1S_0+5s5p ^1P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose nodal point inferred the s-wave scattering length of $a=1.1(2)$ nm. The observed PA resonances also determined a precise lifetime of the $^1P_1$ state to be 5.263(4) ns.We have investigated the photoassociation (PA) spectra of ultracold $^{88}$Sr atoms near the $5s^2 ^1S_0+5s5p ^1P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose nodal point inferred the s-wave scattering length of $a=1.1(2)$ nm. The observed PA resonances also determined a precise lifetime of the $^1P_1$ state to be 5.263(4) ns.

arXiv:physics/0501053Jan 11, 20051 citation

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

We demonstrate photoassociation (PA) of ultracold fermionic

^{87}\mathrm{Sr}

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

^{1}S_{0}+^{1}S_{0}

ground-state potential. Similar measurements and analysis were performed for the bosonic isotopes

^{84}\mathrm{Sr}

and

^{86}\mathrm{Sr}

, allowing a combined analysis of the long-range portion of the excited-state potential and determination of the

5s5p\phantom{\rule{0.16em}{0ex}}^{1}P_{1}

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.

We have investigated photoassociation (PA) spectra of ultracold

^{88}\mathrm{Sr}

atoms near the

5{s}^{2}\phantom{\rule{0.2em}{0ex}}^{1}S_{0}+5s5p\phantom{\rule{0.2em}{0ex}}^{1}P_{1}

atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose last nodal point was determined to be

{r}_{0}=3.78(18)\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

. The PA lines also determined a precise lifetime of the

^{1}P_{1}

state to be

5.263(4)\phantom{\rule{0.3em}{0ex}}\mathrm{ns}

We report photoassociation spectroscopy of ultracold

^{86}\mathrm{Sr}

atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the

{}^{1}{S}_{0}+{}^{3}{P}_{1}

asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date:

^{84}\mathrm{Sr},^{86}\mathrm{Sr}

, and

^{88}\mathrm{Sr}

. We attribute that to the recently discovered avoided crossing between the

{}^{1}{S}_{0}+{}^{3}{P}_{1}

{0}_{u}^{+}

$({}^{3}{\ensuremath{\Pi}}_{u})$ and

{}^{1}{S}_{0}+{}^{1}{D}_{2}

{0}_{u}^{+}

$({}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available

{0}_{u}^{+}

and

{1}_{u}

bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the

{0}_{u}^{+}

and

{1}_{u}

curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two $\ensuremath{-}8$-GHz bound states in

^{88}\mathrm{Sr}

over the previously used model potentials. We show that one of the recently reported energy levels in

^{84}\mathrm{Sr}

does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients

{C}_{6}({0}_{u}^{+})=3868(50)

a.u. and

{C}_{6}({1}_{u})=4085(50)

a.u. are reported.

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.

{0}_{u}^{+}

purely long-range potential well is very good. The results yield a determination of the lifetime of the

2\phantom{\rule{0.3em}{0ex}}^{3}P

atomic state.

We have investigated the photoassociation (PA) spectra of ultracold

^{88}

Sr atoms near the $5s^2 ^1S_0+5s5p ^1P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose nodal point inferred the s-wave scattering length of

a=1.1(2)

nm. The observed PA resonances also determined a precise lifetime of the

^1P_1

state to be 5.263(4) ns.

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.