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.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:0810.5703New Journal of PhysicsMay 14, 200937 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.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 ASep 14, 200915 citations

Electronic properties of francium diatomic compounds and prospects for cold molecule formation

M Aymar, Olivier Dulieu, Fernand Spiegelman

In this work, we investigate the possibility of creating cold Fr 2 , RbFr and CsFr molecules through the photoassociation of cold atoms. Potential curves, permanent and transition dipole moments for the francium dimer and for the RbFr and RbCs molecules are determined for the first time. The francium atom is modelled as one valence electron moving in the field of the Fr + core, which is described by a new pseudopotential with averaged relativistic effects, and including effective core-polarization potential. The molecular calculations are performed for both the ionic species Fr + 2 , RbFr + , CsFr + and the corresponding neutrals, through the CIPSI quantum chemistry package where we used new extended Gaussian basis sets for Rb, Cs and Fr atoms. As no experimental data are available, we discuss our results by comparison with the Rb 2 , Cs 2 and RbCs systems. The dipole moment of CsFr reveals an electron transfer yielding a Cs + Fr − arrangement, while in all other mixed alkali pairs the electron is transferred towards the lighter species. Finally, the perturbative treatment of the spin–orbit coupling at large distances predicts that in contrast with Rb 2 and Cs 2 no double-well excited potential should be present in Fr 2 , probably preventing an efficient formation of cold dimers via the photoassociation of cold francium atoms.In this work, we investigate the possibility of creating cold Fr 2 , RbFr and CsFr molecules through the photoassociation of cold atoms. Potential curves, permanent and transition dipole moments for the francium dimer and for the RbFr and RbCs molecules are determined for the first time. The francium atom is modelled as one valence electron moving in the field of the Fr + core, which is described by a new pseudopotential with averaged relativistic effects, and including effective core-polarization potential. The molecular calculations are performed for both the ionic species Fr + 2 , RbFr + , CsFr + and the corresponding neutrals, through the CIPSI quantum chemistry package where we used new extended Gaussian basis sets for Rb, Cs and Fr atoms. As no experimental data are available, we discuss our results by comparison with the Rb 2 , Cs 2 and RbCs systems. The dipole moment of CsFr reveals an electron transfer yielding a Cs + Fr − arrangement, while in all other mixed alkali pairs the electron is transferred towards the lighter species. Finally, the perturbative treatment of the spin–orbit coupling at large distances predicts that in contrast with Rb 2 and Cs 2 no double-well excited potential should be present in Fr 2 , probably preventing an efficient formation of cold dimers via the photoassociation of cold francium atoms.

arXiv:quant-ph/0604144Journal of Physics B Atomic Molecular and Optical PhysicsSep 25, 200645 citations

Spin-orbit coupling effect in the low-lying states of Rb

_{2}

, Cs

_{2}

and RbCs molecules

Spin-orbit coupling effect on the 2$^{3}\Pi $ state of

^{39}

^{85}

\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.