Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0810.5703 · New Journal of Physics

Stimulating the production of deeply bound RbCs molecules with laser pulses: the role of spin–orbit coupling in forming ultracold molecules

Subhas Ghosal, Richard J Doyle, Christiane P. Koch, Jeremy M. Hutson

Published May 14, 2009• 37 citations
arXivHTMLPDF

Abstract

We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb 2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85 Rb and 133 Cs atoms colliding on the X 1 Σ + potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P 1/2 ) asymptote. We explore the nature of the Ω=0 + levels in this region, which have mixed A 1 Σ + and b 3 Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm −1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb 2 system; this is mostly because of the absence of an R −3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb 2 , the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm −1 . The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.

DOI
10.1088/1367-2630/11/5/055011

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.

arXiv:1111.3503•Laser Physics•Sep 3, 2012•23 citations

Formation of ultracold metastable RbCs molecules by short-range photoassociation

C. Gabbanini, Olivier Dulieu

Ultracold metastable RbCs molecules are observed in a double species magneto-optical trap through photoassociation near the Rb(5S(1/2)) + Cs(6P(3/2)) dissociation limit followed by radiative stabilization. The molecules are formed in their lowest triplet electronic state and are detected by resonance enhanced two-photon ionization through the previously unobserved (3)(3)Π ← a (3)Σ(+) band. The large rotational structure of the observed photoassociation lines is assigned to the lowest vibrational levels of the 0(+) or 0(-) excited states correlated to the Rb(5P(1/2)) + Cs(6S(1/2)) dissociation limit. This demonstrates the possibility of inducing direct photoassociation in heteronuclear alkali-metal molecules at a short internuclear distance, as pointed out earlier [J. Deiglmayr et al., Phys. Rev. Lett., 2008, 101, 13304].

arXiv:1107.0547•Physical Chemistry Chemical Physics•Jan 1, 2011•47 citations

Photoassociative Production and Detection of Ultracold Polar RbCs Molecules

Zhonghua Ji, Hongshan Zhang, Jizhou Wu +6 more

We have produced ultracold polar RbCs molecules via photoassociation starting from laser-cooled 85 Rb and 133 Cs atoms in a dual-species, forced dark magneto-optical trap. The formed electronically excited RbCs* molecules correlated to the Rb(5S 1/2 ) + Cs(6P 1/2 ) dissociation limit are observed by trap loss spectroscopy. Following the decay of these excited RbCs* molecules, the formed ground state molecules are directly ionized by a two-photon single-color pulse dye laser, which is a new ionization mechanism for ground state RbCs molecules and thence detected by time-of-flight mass spectroscopy.

Chinese Physics Letters•Aug 1, 2011•8 citations

Production of Ultracold, Polar RbCs* Molecules via Photoassociation

Andrew J. Kerman, Jeremy Sage, Sunil Sainis +2 more

We have produced ultracold, polar ${\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}$ molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the ${\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}$ molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound $X\text{ }^{1}\ensuremath{\Sigma}^{+}$ ground-state RbCs vibrational levels as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.

arXiv:physics/0308020•Physical Review Letters•Jan 23, 2004•206 citations

Resonant coupling effects on the photoassociation of ultracold Rb and Cs atoms

B. E. Londoño, Jorge Mahecha, Eliane Luc-Koenig +1 more

In the polar RbCs molecule, the strong spin-orbit coupling between the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ diabatic electronic states correlated to the $\mathrm{Rb}(5s)\mathrm{Cs}(6p)$ dissociation limit is at the origin of a global mixing of the two vibrational ${0}^{+}({P}_{1∕2,3∕2})$ series coupled radiatively to both $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ states. This so-called ``resonant coupling'' plays a crucial role in the formation of ultracold stable RbCs molecules through photoassociation into ${0}^{+}$ levels followed by stabilization through spontaneous emission. We analyze quantitatively the mechanisms of photoassociation and stabilization through ${0}^{+}$ levels, starting from and leading to either the singlet or the triplet states and we compare the efficiency of the four paths leading to the formation of stable RbCs molecules. Comparison between the two isotopomers $^{87}\mathrm{Rb}^{133}\mathrm{Cs}$ and $^{85}\mathrm{Rb}^{133}\mathrm{Cs}$ is also reported: the overall process of formation of stable molecules is one order of magnitude larger for $^{87}\mathrm{Rb}\mathrm{Cs}$. The simple two-channel model presented here yields the general rules for a standard analysis of the effects of resonant coupling between electronic states. To underline the specificity of heteronuclear molecules, the ${0}^{+}$ coupled system of the RbCs molecule is compared to its analog, the ${0}_{u}^{+}$ system of the ${\mathrm{Rb}}_{2}$ molecule.

Physical Review A•Sep 14, 2009•15 citations

Investigation on ultracold RbCs molecules in (2)0+ long-range state below the Rb(5S1/2) + Cs(6P1/2) asymptote by high resolution photoassociation spectroscopy

Jinpeng Yuan, Zhonghua Ji, Zhonghao Li +3 more

We present high resolution photoassociation spectroscopy of RbCs molecules in (2)0(+) long-range state below the Rb(5S1/2) + Cs(6P1/2) asymptote and derive the corresponding C6 coefficient, which is used to revise the potential energy curves. The excited state molecules are produced in a dual-species dark spontaneous force optical trap and detected by ionizing ground state molecules after spontaneous decay, using a high sensitive time-of-flight mass spectrum. With the help of resonance-enhanced two-photon ionization technique, we obtain considerable high resolution photoassociation spectrum with rovibrational states, some of which have never been observed before. By applying the LeRoy-Bernstein method, we assign the vibrational quantum numbers and deduce C6 coefficient, which agrees with the theoretical value of A(1)Σ(+) state correlated to Rb(5S1/2) + Cs(6P1/2) asymptote. The obtained C6 coefficient is used to revise the long-range potential energy curve for (2)0(+) state, which possesses unique A - b mixing characteristic and can be a good candidate for the production of absolutely ground state molecule.

The Journal of Chemical Physics•Jul 28, 2015•7 citations
We investigate the possibility of forming deeply bound ultracold RbCs molecules by a two-color photoassociation experiment. We compare the results with those for Rb 2 in order to understand the characteristic differences between heteronuclear and homonuclear molecules. The major differences arise from the different long-range potential for excited states. Ultracold 85 Rb and 133 Cs atoms colliding on the X 1 Σ + potential curve are initially photoassociated to form excited RbCs molecules in the region below the Rb(5S)+Cs(6P 1/2 ) asymptote. We explore the nature of the Ω=0 + levels in this region, which have mixed A 1 Σ + and b 3 Π character. We then study the quantum dynamics of RbCs by a time-dependent wavepacket (TDWP) approach. A wavepacket is formed by exciting a few vibronic levels and is allowed to propagate on the coupled electronic potential energy curves. We calculate the time dependence of the overlap between the wavepacket and ground-state vibrational levels. For a detuning of 7.5 cm −1 from the atomic line, the wavepacket for RbCs reaches the short-range region in about 13 ps, which is significantly faster than for the homonuclear Rb 2 system; this is mostly because of the absence of an R −3 long-range tail in the excited-state potential curves for heteronuclear systems. We give a simple semiclassical formula that relates the time taken to the long-range potential parameters. For RbCs, in contrast to Rb 2 , the excited-state wavepacket shows a substantial peak in singlet density near the inner turning point, and this produces a significant probability of de-excitation to form ground-state molecules bound by up to 1500 cm −1 . The short-range peak depends strongly on non-adiabatic coupling and is reduced if the strength of the spin–orbit coupling is increased. Our analysis of the role of spin–orbit coupling concerns the character of the mixed states in general and is important for both photoassociation and stimulated Raman de-excitation.
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.
Ultracold metastable RbCs molecules are observed in a double species magneto-optical trap through photoassociation near the Rb(5S(1/2)) + Cs(6P(3/2)) dissociation limit followed by radiative stabilization. The molecules are formed in their lowest triplet electronic state and are detected by resonance enhanced two-photon ionization through the previously unobserved (3)(3)Π ← a (3)Σ(+) band. The large rotational structure of the observed photoassociation lines is assigned to the lowest vibrational levels of the 0(+) or 0(-) excited states correlated to the Rb(5P(1/2)) + Cs(6S(1/2)) dissociation limit. This demonstrates the possibility of inducing direct photoassociation in heteronuclear alkali-metal molecules at a short internuclear distance, as pointed out earlier [J. Deiglmayr et al., Phys. Rev. Lett., 2008, 101, 13304].
We have produced ultracold polar RbCs molecules via photoassociation starting from laser-cooled 85 Rb and 133 Cs atoms in a dual-species, forced dark magneto-optical trap. The formed electronically excited RbCs* molecules correlated to the Rb(5S 1/2 ) + Cs(6P 1/2 ) dissociation limit are observed by trap loss spectroscopy. Following the decay of these excited RbCs* molecules, the formed ground state molecules are directly ionized by a two-photon single-color pulse dye laser, which is a new ionization mechanism for ground state RbCs molecules and thence detected by time-of-flight mass spectroscopy.
We have produced ultracold, polar RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecules via photoassociation in a laser-cooled mixture of Rb and Cs atoms. Using a model of the RbCs∗{\mathrm{R}\mathrm{b}\mathrm{C}\mathrm{s}}^{*}RbCs∗ molecular interaction which reproduces the observed rovibrational structure, we infer decay rates in our experiments into deeply bound $X\text{ }^{1}\ensuremath{\Sigma}^{+}$ ground-state RbCs vibrational levels as high as $5\ifmmode\times\else\texttimes\fi{}{10}^{5}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ per level. Population in such deeply bound levels could be efficiently transferred to the vibrational ground state using a single stimulated Raman transition, opening the possibility to create large samples of stable, ultracold polar molecules.
In the polar RbCs molecule, the strong spin-orbit coupling between the $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $b\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}$ diabatic electronic states correlated to the Rb(5s)Cs(6p)\mathrm{Rb}(5s)\mathrm{Cs}(6p)Rb(5s)Cs(6p) dissociation limit is at the origin of a global mixing of the two vibrational 0+(P1∕2,3∕2){0}^{+}({P}_{1∕2,3∕2})0+(P1∕2,3∕2​) series coupled radiatively to both $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}$ and $a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}$ states. This so-called ``resonant coupling'' plays a crucial role in the formation of ultracold stable RbCs molecules through photoassociation into 0+{0}^{+}0+ levels followed by stabilization through spontaneous emission. We analyze quantitatively the mechanisms of photoassociation and stabilization through 0+{0}^{+}0+ levels, starting from and leading to either the singlet or the triplet states and we compare the efficiency of the four paths leading to the formation of stable RbCs molecules. Comparison between the two isotopomers 87Rb133Cs^{87}\mathrm{Rb}^{133}\mathrm{Cs}87Rb133Cs and 85Rb133Cs^{85}\mathrm{Rb}^{133}\mathrm{Cs}85Rb133Cs is also reported: the overall process of formation of stable molecules is one order of magnitude larger for 87RbCs^{87}\mathrm{Rb}\mathrm{Cs}87RbCs. The simple two-channel model presented here yields the general rules for a standard analysis of the effects of resonant coupling between electronic states. To underline the specificity of heteronuclear molecules, the 0+{0}^{+}0+ coupled system of the RbCs molecule is compared to its analog, the 0u+{0}_{u}^{+}0u+​ system of the Rb2{\mathrm{Rb}}_{2}Rb2​ molecule.
We present high resolution photoassociation spectroscopy of RbCs molecules in (2)0(+) long-range state below the Rb(5S1/2) + Cs(6P1/2) asymptote and derive the corresponding C6 coefficient, which is used to revise the potential energy curves. The excited state molecules are produced in a dual-species dark spontaneous force optical trap and detected by ionizing ground state molecules after spontaneous decay, using a high sensitive time-of-flight mass spectrum. With the help of resonance-enhanced two-photon ionization technique, we obtain considerable high resolution photoassociation spectrum with rovibrational states, some of which have never been observed before. By applying the LeRoy-Bernstein method, we assign the vibrational quantum numbers and deduce C6 coefficient, which agrees with the theoretical value of A(1)Σ(+) state correlated to Rb(5S1/2) + Cs(6P1/2) asymptote. The obtained C6 coefficient is used to revise the long-range potential energy curve for (2)0(+) state, which possesses unique A - b mixing characteristic and can be a good candidate for the production of absolutely ground state molecule.