arXiv:1203.4552 · Physical Review A

Formation of deeply bound ultracold Sr 2 molecules by photoassociation near the 1S+3P1 intercombination line

Wojciech Skomorowski, Robert Moszyński, Christiane P. Koch

Published Apr 17, 2012• 28 citations

Abstract

We predict feasibility of the photoassociative formation of Sr${}_{2}$ molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the $c\phantom{\rule{0.16em}{0ex}}$${}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}$, $A\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$, and $B\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}$ states. It creates not only an effective dipole moment allowing free-to-bound transitions near the ${}^{1}\phantom{\rule{-0.16em}{0ex}}S+{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground $X\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}$ potential, with ${v}^{\ensuremath{'}\ensuremath{'}}$ as low as ${v}^{\ensuremath{'}\ensuremath{'}}=6$. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited-state levels that have the largest bound-to-bound transition moments to deeply bound ground-state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited-state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr${}_{2}$ molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.

DOI: 10.1103/physreva.85.043414

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Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

Michał Tomza, Filip Pawłowski, Małgorzata Jeziorska +2 more

arXiv:1104.3015Physical Chemistry Chemical PhysicsJan 1, 201141 citations

Short-pulse photoassociation in rubidium below the D1 line

Christiane P. Koch, Ronnie Kosloff, Françoise Masnou-Seeuws

arXiv:physics/0511235Physical Review AApr 13, 200673 citations

Proposal for the formation of ultracold deeply bound RbSr dipolar molecules by all-optical methods

Adrien Devolder, Eliane Luc-Koenig, Osman Atabek +2 more

arXiv:1806.10346Physical Review ANov 9, 201814 citations

Enhancement of the formation of ultracold Rb285 molecules due to resonant coupling

Hyewon Pechkis, Dajun Wang, Yanyan Huang +4 more

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Optical Production of Stable Ultracold Sr288 Molecules

Gael Reinaudi, C. B. Osborn, Mickey McDonald +2 more

arXiv:1206.0417Physical Review LettersSep 13, 201283 citations

Prospects for application of ultracold Sr2 molecules in precision measurements

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arXiv:0811.3971Physical Review AJan 8, 200948 citations

arXiv:1203.4552 · Physical Review A

Formation of deeply bound ultracold Sr 2 molecules by photoassociation near the 1S+3P1 intercombination line

Wojciech Skomorowski, Robert Moszyński, Christiane P. Koch

Published Apr 17, 2012• 28 citations

arXiv HTML PDF

Abstract

We predict feasibility of the photoassociative formation of Sr

{}_{2}

molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the

c\phantom{\rule{0.16em}{0ex}}$${}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}

A\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}

, and

B\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}

states. It creates not only an effective dipole moment allowing free-to-bound transitions near the

{}^{1}\phantom{\rule{-0.16em}{0ex}}S+{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}

intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground

X\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}

potential, with

{v}^{\ensuremath{'}\ensuremath{'}}

as low as

{v}^{\ensuremath{'}\ensuremath{'}}=6

. The spin-orbit interaction is responsible for both optical pathways. Therefore, those excited-state levels that have the largest bound-to-bound transition moments to deeply bound ground-state levels also exhibit a sufficient photoassociation probability, comparable to that of the lowest weakly bound excited-state level previously observed by Zelevinsky et al. [Phys. Rev. Lett. 96, 203201 (2006)]. Our study paves the way for an efficient photoassociative production of Sr

{}_{2}

molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.

DOI: 10.1103/physreva.85.043414

Related papers

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

Michał Tomza, Filip Pawłowski, Małgorzata Jeziorska +2 more

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

arXiv:1104.3015Physical Chemistry Chemical PhysicsJan 1, 201141 citations

Short-pulse photoassociation in rubidium below the D1 line

Christiane P. Koch, Ronnie Kosloff, Françoise Masnou-Seeuws

Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5{P}_{1∕2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1∕{R}^{3}$ potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the ${0}_{u}^{+}$ states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.Photoassociation of two ultracold rubidium atoms and the subsequent formation of stable molecules in the singlet ground and lowest triplet states is investigated theoretically. The method employs laser pulses inducing transitions via excited states correlated to the $5S+5{P}_{1∕2}$ asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range $1∕{R}^{3}$ potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the ${0}_{u}^{+}$ states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

arXiv:physics/0511235Physical Review AApr 13, 200673 citations

Proposal for the formation of ultracold deeply bound RbSr dipolar molecules by all-optical methods

Adrien Devolder, Eliane Luc-Koenig, Osman Atabek +2 more

Ultracold paramagnetic and polar diatomic molecules are among the promising systems for quantum simulation of lattice-spin models. Unfortunately, their experimental observation is still challenging. Based on our recent ab initio calculations, we analyze the feasibility of all-optical schemes for the formation of ultracold $^{87}\mathrm{Rb}^{84}\mathrm{Sr}$ bosonic molecules. A first possibility is photoassociation followed by spontaneous emission. The photoassociation rate coefficients toward electronic states converging to the $^{87}\mathrm{Rb}(5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2})+^{84}\mathrm{Sr}(5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$ ) asymptotes are particularly small for vibrational levels close to the asymptote. The creation of molecules would be more interesting by using deeply bound levels which preferentially relax to the ${v}^{\ensuremath{'}\ensuremath{'}}=0$ level of the ground state. On the other hand, the photoassociation rate coefficients toward electronic states correlated to the $\mathrm{Rb}(5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2})+\mathrm{Sr}(5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ ) are significant for levels close to the asymptote. The spontaneous emission thus creates weakly bound molecules in a single vibrational level. A second option relies on stimulated Raman adiabatic passage implemented in a tight optical trap. It efficiently creates weakly bound ground-state molecules in a well-defined level, thus providing a promising alternative to magnetic Feshbach resonances for further population transfer toward the absolute ground state of the RbSr molecule.Ultracold paramagnetic and polar diatomic molecules are among the promising systems for quantum simulation of lattice-spin models. Unfortunately, their experimental observation is still challenging. Based on our recent ab initio calculations, we analyze the feasibility of all-optical schemes for the formation of ultracold $^{87}\mathrm{Rb}^{84}\mathrm{Sr}$ bosonic molecules. A first possibility is photoassociation followed by spontaneous emission. The photoassociation rate coefficients toward electronic states converging to the $^{87}\mathrm{Rb}(5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2})+^{84}\mathrm{Sr}(5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}$) asymptotes are particularly small for vibrational levels close to the asymptote. The creation of molecules would be more interesting by using deeply bound levels which preferentially relax to the ${v}^{\ensuremath{'}\ensuremath{'}}=0$ level of the ground state. On the other hand, the photoassociation rate coefficients toward electronic states correlated to the $\mathrm{Rb}(5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2})+\mathrm{Sr}(5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$) are significant for levels close to the asymptote. The spontaneous emission thus creates weakly bound molecules in a single vibrational level. A second option relies on stimulated Raman adiabatic passage implemented in a tight optical trap. It efficiently creates weakly bound ground-state molecules in a well-defined level, thus providing a promising alternative to magnetic Feshbach resonances for further population transfer toward the absolute ground state of the RbSr molecule.

arXiv:1806.10346Physical Review ANov 9, 201814 citations

Enhancement of the formation of ultracold Rb285 molecules due to resonant coupling

Hyewon Pechkis, Dajun Wang, Yanyan Huang +4 more

We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state $^{85}\mathrm{Rb}_{2}$ . Ultracold ${\mathrm{Rb}}_{2}$ molecules are formed by photoassociation (PA) to a coupled pair of ${0}_{u}^{+}$ states, ${0}_{u}^{+}({P}_{1∕2})$ and ${0}_{u}^{+}({P}_{3∕2})$ , in the region below the $5S+5{P}_{1∕2}$ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$. The population distribution of these $X$ -state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. We find that the populations of vibrational levels ${v}^{\ensuremath{''}}=112--116$ are far larger than can be accounted for by the Franck-Condon factors for ${0}_{u}^{+}({P}_{1∕2})\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions with the ${0}_{u}^{+}({P}_{1∕2})$ state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of ${0}_{u}^{+}$ state vibrational levels. Both of these effects are explained by a calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two ${0}_{u}^{+}$ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state $^{85}\mathrm{Rb}_{2}$. Ultracold ${\mathrm{Rb}}_{2}$ molecules are formed by photoassociation (PA) to a coupled pair of ${0}_{u}^{+}$ states, ${0}_{u}^{+}({P}_{1∕2})$ and ${0}_{u}^{+}({P}_{3∕2})$, in the region below the $5S+5{P}_{1∕2}$ limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$. The population distribution of these $X$-state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. We find that the populations of vibrational levels ${v}^{\ensuremath{''}}=112--116$ are far larger than can be accounted for by the Franck-Condon factors for ${0}_{u}^{+}({P}_{1∕2})\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions with the ${0}_{u}^{+}({P}_{1∕2})$ state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of ${0}_{u}^{+}$ state vibrational levels. Both of these effects are explained by a calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two ${0}_{u}^{+}$ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.

arXiv:0707.2401Physical Review AAug 22, 200733 citations

Optical Production of Stable Ultracold Sr288 Molecules

Gael Reinaudi, C. B. Osborn, Mickey McDonald +2 more

We have produced large samples of stable ultracold (88)Sr(2) molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a near-intercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-Q molecular vibronic resonance. This is the first of two steps needed to create deeply bound (88)Sr(2) for frequency metrology and ultracold chemistry.We have produced large samples of stable ultracold (88)Sr(2) molecules in the electronic ground state in an optical lattice. The fast, all-optical method of molecule creation involves a near-intercombination-line photoassociation pulse followed by spontaneous emission with a near-unity Franck-Condon factor. The detection uses excitation to a weakly bound electronically excited vibrational level corresponding to a very large dimer and yields a high-Q molecular vibronic resonance. This is the first of two steps needed to create deeply bound (88)Sr(2) for frequency metrology and ultracold chemistry.

arXiv:1206.0417Physical Review LettersSep 13, 201283 citations

Prospects for application of ultracold Sr2 molecules in precision measurements

Svetlana Kotochigova, Tanya Zelevinsky, Jun Ye

Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the ${\mathrm{Sr}}_{2}$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. ${\mathrm{Sr}}_{2}$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.Precision measurements with ultracold molecules require development of robust and sensitive techniques to produce and interrogate the molecules. With this goal, we theoretically analyze factors that affect frequency measurements between rovibrational levels of the ${\mathrm{Sr}}_{2}$ molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio. ${\mathrm{Sr}}_{2}$ is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.

arXiv:0811.3971Physical Review AJan 8, 200948 citations

We predict feasibility of the photoassociative formation of Sr

{}_{2}

molecules in arbitrary vibrational levels of the electronic ground state based on state-of-the-art ab initio calculations. Key is the strong spin-orbit interaction between the

c\phantom{\rule{0.16em}{0ex}}$${}^{3}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Pi}}_{u}

A\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}

, and

B\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{u}^{+}

states. It creates not only an effective dipole moment allowing free-to-bound transitions near the

{}^{1}\phantom{\rule{-0.16em}{0ex}}S+{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}

intercombination line but also facilitates bound-to-bound transitions via resonantly coupled excited-state levels to deeply bound levels of the ground

X\phantom{\rule{0.16em}{0ex}}$${}^{1}\phantom{\rule{-0.16em}{0ex}}{\ensuremath{\Sigma}}_{g}^{+}

potential, with

{v}^{\ensuremath{'}\ensuremath{'}}

as low as

{v}^{\ensuremath{'}\ensuremath{'}}=6

{}_{2}

molecules in ground-state levels suitable for experiments testing the electron-to-proton mass ratio.

5S+5{P}_{1∕2}

asymptote. Weakly bound molecules in the singlet ground or lowest triplet state can be created by a single pulse while the formation of more deeply bound molecules requires a two-color pump-dump scenario. More deeply bound molecules in the singlet ground or lowest triplet state can be produced only if efficient mechanisms for both pump and dump steps exist. While long-range

1∕{R}^{3}

potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the

{0}_{u}^{+}

states. Molecules in the singlet ground state bound by a few wave numbers can thus be formed. This provides a promising first step toward ground-state molecules which are ultracold in both translational and vibrational degrees of freedom.

^{87}\mathrm{Rb}^{84}\mathrm{Sr}

bosonic molecules. A first possibility is photoassociation followed by spontaneous emission. The photoassociation rate coefficients toward electronic states converging to the

^{87}\mathrm{Rb}(5s\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2})+^{84}\mathrm{Sr}(5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{0,1,2}

) asymptotes are particularly small for vibrational levels close to the asymptote. The creation of molecules would be more interesting by using deeply bound levels which preferentially relax to the ${v}^{\ensuremath{'}\ensuremath{'}}=0$ level of the ground state. On the other hand, the photoassociation rate coefficients toward electronic states correlated to the

\mathrm{Rb}(5p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2,3/2})+\mathrm{Sr}(5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}

) are significant for levels close to the asymptote. The spontaneous emission thus creates weakly bound molecules in a single vibrational level. A second option relies on stimulated Raman adiabatic passage implemented in a tight optical trap. It efficiently creates weakly bound ground-state molecules in a well-defined level, thus providing a promising alternative to magnetic Feshbach resonances for further population transfer toward the absolute ground state of the RbSr molecule.

We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state

^{85}\mathrm{Rb}_{2}

. Ultracold

{\mathrm{Rb}}_{2}

molecules are formed by photoassociation (PA) to a coupled pair of

{0}_{u}^{+}

states,

{0}_{u}^{+}({P}_{1∕2})

and

{0}_{u}^{+}({P}_{3∕2})

, in the region below the

5S+5{P}_{1∕2}

limit. Subsequent radiative decay produces high vibrational levels of the ground state, $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$. The population distribution of these

X

-state vibrational levels is monitored by resonance-enhanced two-photon ionization through the $2\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ state. We find that the populations of vibrational levels ${v}^{\ensuremath{''}}=112--116$ are far larger than can be accounted for by the Franck-Condon factors for ${0}_{u}^{+}({P}_{1∕2})\ensuremath{\rightarrow}X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transitions with the

{0}_{u}^{+}({P}_{1∕2})

state treated as a single channel. Further, the ground-state molecule population exhibits oscillatory behavior as the PA laser is tuned through a succession of

{0}_{u}^{+}

state vibrational levels. Both of these effects are explained by a calculation of transition amplitudes that includes the resonant character of the spin-orbit coupling of the two

{0}_{u}^{+}

states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.

{\mathrm{Sr}}_{2}

molecule in the electronic ground state. This measurement can be used to constrain the possible time variation of the proton-electron mass ratio.

{\mathrm{Sr}}_{2}

is expected to be a strong candidate for achieving high precision due to the spinless nature and ease of cooling and perturbation-free trapping of Sr [T. Zelevinsky et al., Phys. Rev. Lett. 100, 043201 (2008)]. The analysis includes calculations of two-photon transition dipole moments between deeply and weakly bound vibrational levels, lifetimes of intermediate excited states, and Stark shifts of the vibrational levels by the optical lattice field, including possibilities of Stark-cancellation trapping.