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

Physical Review A

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

B. E. Londoño, Jorge Mahecha, Eliane Luc-Koenig, A. Crubellier

Published Sep 14, 2009• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.80.032511

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

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.

arXiv:0707.2401•Physical Review A•Aug 22, 2007•33 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

Experimental study of the formation of ultracold RbCs molecules by short-range photoassociation

A. Fioretti, C. Gabbanini

We have experimentally studied the formation of ultracold RbCs molecules by photoassociation at short internuclear range followed by spontaneous emission. The observation of new excited levels with respect to our previous work [Gabbanini and Dulieu, Phys. Chem. Chem. Phys. 13, 18905 (2011)] on both sides of the $\text{Rb}(5{S}_{1/2})+\text{Cs}(6{P}_{3/2})$ dissociation limit gives information on the state responsible for molecule formation. The molecules are mainly formed in deeply bound levels of the electronic triplet ground state. The observed photoassociation transitions present differences in terms of saturation.

Physical Review A•May 17, 2013•22 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.

arXiv:physics/0511235•Physical Review A•Apr 13, 2006•73 citations

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 +1 more

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.

arXiv:0810.5703•New Journal of Physics•May 14, 2009•37 citations
In the polar RbCs molecule, the strong spin-orbit coupling between the A1\ensuremathΣ+A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}A1\ensuremathΣ+ and b3\ensuremathΠb\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Pi}b3\ensuremathΠ 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 X1\ensuremathΣ+X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}^{+}X1\ensuremathΣ+ and a3\ensuremathΣ+a\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}^{+}a3\ensuremathΣ+ 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.
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.
We have studied the effect of resonant electronic-state coupling on the formation of ultracold ground-state 85Rb2^{85}\mathrm{Rb}_{2}85Rb2​. Ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ molecules are formed by photoassociation (PA) to a coupled pair of 0u+{0}_{u}^{+}0u+​ states, 0u+(P1∕2){0}_{u}^{+}({P}_{1∕2})0u+​(P1∕2​) and 0u+(P3∕2){0}_{u}^{+}({P}_{3∕2})0u+​(P3∕2​), in the region below the 5S+5P1∕25S+5{P}_{1∕2}5S+5P1∕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 XXX-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 0u+(P1∕2){0}_{u}^{+}({P}_{1∕2})0u+​(P1∕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 0u+{0}_{u}^{+}0u+​ 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 0u+{0}_{u}^{+}0u+​ states. The resulting enhancement of more deeply bound ground-state molecule formation will be useful for future experiments on ultracold molecules.
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 experimentally studied the formation of ultracold RbCs molecules by photoassociation at short internuclear range followed by spontaneous emission. The observation of new excited levels with respect to our previous work [Gabbanini and Dulieu, Phys. Chem. Chem. Phys. 13, 18905 (2011)] on both sides of the Rb(5S1/2)+Cs(6P3/2)\text{Rb}(5{S}_{1/2})+\text{Cs}(6{P}_{3/2})Rb(5S1/2​)+Cs(6P3/2​) dissociation limit gives information on the state responsible for molecule formation. The molecules are mainly formed in deeply bound levels of the electronic triplet ground state. The observed photoassociation transitions present differences in terms of saturation.
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+5P1∕25S+5{P}_{1∕2}5S+5P1∕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∕R31∕{R}^{3}1∕R3 potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the 0u+{0}_{u}^{+}0u+​ 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.
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.