Physical Review A

Near-threshold photoassociation of 87Rb2

M. Kemmann, Ivan Mistrík, S. Nußmann, Hanspeter Helm, Carl J. Williams, Paul S. Julienne

Published Feb 26, 2004• 37 citations

Abstract

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.

DOI: 10.1103/physreva.69.022715

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Formation of ultracold RbCs molecules by photoassociation

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arXiv:1111.3503Laser PhysicsSep 3, 201223 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

Physical Review AJul 28, 200622 citations

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

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Study of Rb2 Long-Range States by High-Resolution Photoassociation Spectroscopy

Robert A. Cline, Joseph D. Miller, Daniel J. Heinzen

Physical Review LettersAug 1, 1994140 citations

Photoassociation spectroscopy of weakly bound $^{87}Rb_{2}$ molecules near $5P_{1/2} +5S_{1/2}$ threshold by optical Bragg scattering in Bose-Einstein condensates

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PHOTOASSOCIATION SPECTROSCOPY OF ${^{85}}Rb_{2}$ NEAR ITS DISSOCIATION LIMIT

R. S. Freeland, Ph. W. Courteille, Chin‐Chun Tsai +4 more

Jan 1, 19980 citations

Physical Review A

Near-threshold photoassociation of 87Rb2

M. Kemmann, Ivan Mistrík, S. Nußmann, Hanspeter Helm, Carl J. Williams, Paul S. Julienne

Published Feb 26, 2004• 37 citations

Publisher

Abstract

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.

DOI: 10.1103/physreva.69.022715

Related papers

Formation of ultracold RbCs molecules by photoassociation

Nadia Bouloufa-Maafa, M Aymar, Olivier Dulieu +1 more

The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the 85 Rb(5S 1/2 ) + 133 Cs(6P 3/2 ) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0 + or the 4th 0 − electronic states correlated to the Rb(5P 1/2, 3/2 ) + Cs(6S 1/2 ) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state.The formation of ultracold metastable RbCs molecules is observed in a double species magneto-optical trap through photoassociation below the 85 Rb(5S 1/2 ) + 133 Cs(6P 3/2 ) dissociation limit followed by spontaneous emission. The molecules are detected by resonance enhanced two-photon ionization. Using accurate quantum chemistry calculations of the potential energy curves and transition dipole moment, we interpret the observed photoassociation process as occurring at short internuclear distance, in contrast with most previous cold atom photoassociation studies. The vibrational levels excited by photoassociation belong to the 5th 0 + or the 4th 0 − electronic states correlated to the Rb(5P 1/2, 3/2 ) + Cs(6S 1/2 ) dissociation limit. The computed vibrational distribution of the produced molecules shows that they are stabilized in deeply bound vibrational states of the lowest triplet state. We also predict that a noticeable fraction of molecules is produced in the lowest level of the electronic ground state.

arXiv:1111.3503Laser PhysicsSep 3, 201223 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

Study of Rb2 Long-Range States by High-Resolution Photoassociation Spectroscopy

Robert A. Cline, Joseph D. Miller, Daniel J. Heinzen

We study the states of ${\mathrm{Rb}}_{2}$ that lie within 35 ${\mathrm{cm}}^{\ensuremath{-}1}$ of the ${5}^{2}{S}_{\frac{1}{2}}+{5}^{2}{P}_{\frac{3}{2}}$ dissociation limit with photoassociation spectroscopy of laser-cooled Rb atoms. We observe the rotationally resolved bound levels of the novel ${0}_{g}^{\ensuremath{-}}$ "pure long-range" state, which has an inner turning point beyond 25 bohrs. We also identify levels belonging to ${1}_{g}$ and ${0}_{\ensuremath{\mu}}^{+}$ states and find that the ${0}_{\ensuremath{\mu}}^{+}$ levels are broadened by predissociation. With our new method, excited molecular states with a binding energy from less than 0.3 to more than 1000 ${\mathrm{cm}}^{\ensuremath{-}1}$ can be studied with a resolution better than 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$.We study the states of ${\mathrm{Rb}}_{2}$ that lie within 35 ${\mathrm{cm}}^{\ensuremath{-}1}$ of the ${5}^{2}{S}_{\frac{1}{2}}+{5}^{2}{P}_{\frac{3}{2}}$ dissociation limit with photoassociation spectroscopy of laser-cooled Rb atoms. We observe the rotationally resolved bound levels of the novel ${0}_{g}^{\ensuremath{-}}$ "pure long-range" state, which has an inner turning point beyond 25 bohrs. We also identify levels belonging to ${1}_{g}$ and ${0}_{\ensuremath{\mu}}^{+}$ states and find that the ${0}_{\ensuremath{\mu}}^{+}$ levels are broadened by predissociation. With our new method, excited molecular states with a binding energy from less than 0.3 to more than 1000 ${\mathrm{cm}}^{\ensuremath{-}1}$ can be studied with a resolution better than 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Physical Review LettersAug 1, 1994140 citations

Photoassociation spectroscopy of weakly bound $^{87}Rb_{2}$ molecules near $5P_{1/2} +5S_{1/2}$ threshold by optical Bragg scattering in Bose-Einstein condensatesPhotoassociation spectroscopy of weakly bound $^{87}Rb_{2}$ molecules near $5P_{1/2} +5S_{1/2}$ threshold by optical Bragg scattering in Bose-Einstein condensates

Khan Sadiq Nawaz, Liangchao Chen, Chengdong Mi +4 more

We report the high resolution photoassociation (PA) spectroscopy of a $^{87}Rb$ Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of $5P_{1/2} +5S_{1/2}$ by optical Bragg scattering. Since the detection of optical Bragg scattering in BEC has a high signal-noise ratio, we obtain the high resolution PA spectrum of excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$ . We compare the results with the conventional method of trap loss and show that the results agree each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and the anomalous strong bound molecular lines at the atomic transition from $|F=1\rangle$ to $|F^{\prime}=2\rangle$ . The observed excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$ are never reported before, which will help to further improve the long range bound state models near the dissociation limit.We report the high resolution photoassociation (PA) spectroscopy of a $^{87}Rb$ Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of $5P_{1/2} +5S_{1/2}$ by optical Bragg scattering. Since the detection of optical Bragg scattering in BEC has a high signal-noise ratio, we obtain the high resolution PA spectrum of excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$. We compare the results with the conventional method of trap loss and show that the results agree each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and the anomalous strong bound molecular lines at the atomic transition from $|F=1\rangle$ to $|F^{\prime}=2\rangle$. The observed excited molecular states in the range of $\pm1$ GHz near the dissociation limit of $5P_{1/2} +5S_{1/2}$ are never reported before, which will help to further improve the long range bound state models near the dissociation limit.

arXiv:2010.08964Oct 18, 20200 citations

PHOTOASSOCIATION SPECTROSCOPY OF ${^{85}}Rb_{2}$ NEAR ITS DISSOCIATION LIMITPHOTOASSOCIATION SPECTROSCOPY OF ${^{85}}Rb_{2}$ NEAR ITS DISSOCIATION LIMIT

R. S. Freeland, Ph. W. Courteille, Chin‐Chun Tsai +4 more

We present results which probe the structure of ${^{85}}Rb_{2}$ very near its lowest dissociation limit. To obtain these results, we used two different variations of photoassociation spectroscopy of laser-cooled and trapped ${^{85}}Rb$ atoms. First, we have determined the positions of twelve of the highest vibrational levels of ${^{85}}Rb_{2}$ , all bound by less than $0.7 cm^{-1}$ , with two-color (free-bound-bound) photoassociation spectroscopy. The levels lie in an energy range for which singlet and triplet states are strongly mixed by the hyperfine interaction. We found that we could accurately describe these states with a novel coupled-channels inverse perturbation analysis. In a second experiment, we have carried out Zeeman-resolved photoassociation spectroscopy. This technique allowed us to probe the energy range in the lowest part of the electronic ground state continuum, which lies between the dissociation limits corresponding to different hyperfine states of the separated atoms. With this method, we have observed a Feshbach scattering resonance in the continuum for the first time, which we find can be tuned to zero energy with a magnetic field.We present results which probe the structure of ${^{85}}Rb_{2}$ very near its lowest dissociation limit. To obtain these results, we used two different variations of photoassociation spectroscopy of laser-cooled and trapped ${^{85}}Rb$ atoms. First, we have determined the positions of twelve of the highest vibrational levels of ${^{85}}Rb_{2}$, all bound by less than $0.7 cm^{-1}$, with two-color (free-bound-bound) photoassociation spectroscopy. The levels lie in an energy range for which singlet and triplet states are strongly mixed by the hyperfine interaction. We found that we could accurately describe these states with a novel coupled-channels inverse perturbation analysis. In a second experiment, we have carried out Zeeman-resolved photoassociation spectroscopy. This technique allowed us to probe the energy range in the lowest part of the electronic ground state continuum, which lies between the dissociation limits corresponding to different hyperfine states of the separated atoms. With this method, we have observed a Feshbach scattering resonance in the continuum for the first time, which we find can be tuned to zero energy with a magnetic field.

Jan 1, 19980 citations

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})

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

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.

We study the states of

{\mathrm{Rb}}_{2}

that lie within 35 ${\mathrm{cm}}^{\ensuremath{-}1}$ of the

{5}^{2}{S}_{\frac{1}{2}}+{5}^{2}{P}_{\frac{3}{2}}

dissociation limit with photoassociation spectroscopy of laser-cooled Rb atoms. We observe the rotationally resolved bound levels of the novel ${0}_{g}^{\ensuremath{-}}$ "pure long-range" state, which has an inner turning point beyond 25 bohrs. We also identify levels belonging to

{1}_{g}

and ${0}_{\ensuremath{\mu}}^{+}$ states and find that the ${0}_{\ensuremath{\mu}}^{+}$ levels are broadened by predissociation. With our new method, excited molecular states with a binding energy from less than 0.3 to more than 1000 ${\mathrm{cm}}^{\ensuremath{-}1}$ can be studied with a resolution better than 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Photoassociation spectroscopy of weakly bound

^{87}Rb_{2}

molecules near

5P_{1/2} +5S_{1/2}

threshold by optical Bragg scattering in Bose-Einstein condensates

We report the high resolution photoassociation (PA) spectroscopy of a

^{87}Rb

Bose-Einstein condensate (BEC) to excited molecular states near the dissociation limit of

5P_{1/2} +5S_{1/2}

by optical Bragg scattering. Since the detection of optical Bragg scattering in BEC has a high signal-noise ratio, we obtain the high resolution PA spectrum of excited molecular states in the range of

\pm1

GHz near the dissociation limit of

5P_{1/2} +5S_{1/2}

. We compare the results with the conventional method of trap loss and show that the results agree each other very well. Many interesting phenomena of excited molecular states are observed, such as light-induced frequency shift and the anomalous strong bound molecular lines at the atomic transition from

|F=1\rangle

|F^{\prime}=2\rangle

. The observed excited molecular states in the range of

\pm1

GHz near the dissociation limit of

5P_{1/2} +5S_{1/2}

are never reported before, which will help to further improve the long range bound state models near the dissociation limit.

PHOTOASSOCIATION SPECTROSCOPY OF

{^{85}}Rb_{2}

NEAR ITS DISSOCIATION LIMIT

We present results which probe the structure of

{^{85}}Rb_{2}

very near its lowest dissociation limit. To obtain these results, we used two different variations of photoassociation spectroscopy of laser-cooled and trapped

{^{85}}Rb

atoms. First, we have determined the positions of twelve of the highest vibrational levels of

{^{85}}Rb_{2}

, all bound by less than

0.7 cm^{-1}

, with two-color (free-bound-bound) photoassociation spectroscopy. The levels lie in an energy range for which singlet and triplet states are strongly mixed by the hyperfine interaction. We found that we could accurately describe these states with a novel coupled-channels inverse perturbation analysis. In a second experiment, we have carried out Zeeman-resolved photoassociation spectroscopy. This technique allowed us to probe the energy range in the lowest part of the electronic ground state continuum, which lies between the dissociation limits corresponding to different hyperfine states of the separated atoms. With this method, we have observed a Feshbach scattering resonance in the continuum for the first time, which we find can be tuned to zero energy with a magnetic field.