Physical Review A

Relativisticab initiotreatment of the second-order spin-orbit splitting of the a3Σu+ potential of rubidium and cesium dimers

Svetlana Kotochigova, Eite Tiesinga, Paul S. Julienne

Published Dec 13, 2000• 37 citations

Abstract

We have calculated the splitting between the ${0}_{u}^{\ensuremath{-}}$ and ${1}_{u}$ components of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state of ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$ using a relativistic ab initio configuration-interaction valence bond method. This so-called second-order spin-orbit splitting is entirely due to relativistic correlations within the molecule. Our ab initio nonperturbative splitting is 5 and 2 times larger than perturbative splittings at the inner turning point of the $a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ potential for ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2},$ respectively. In addition, close-coupled nuclear dynamics calculations that estimate the effect of this splitting on experimentally accessible quantities are presented. The splitting affects the collisional loss rate of magnetically trapped ultracold Rb and Cs atoms and the spectroscopic determination of the vibrational structure of ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$ dimers. Agreement with the experimental collisional loss rates of Cs is found.

DOI: 10.1103/physreva.63.012517

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Physical Review A

Relativisticab initiotreatment of the second-order spin-orbit splitting of the a3Σu+ potential of rubidium and cesium dimers

Svetlana Kotochigova, Eite Tiesinga, Paul S. Julienne

Published Dec 13, 2000• 37 citations

Publisher

Abstract

We have calculated the splitting between the

{0}_{u}^{\ensuremath{-}}

and

{1}_{u}

components of the

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

state of

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

using a relativistic ab initio configuration-interaction valence bond method. This so-called second-order spin-orbit splitting is entirely due to relativistic correlations within the molecule. Our ab initio nonperturbative splitting is 5 and 2 times larger than perturbative splittings at the inner turning point of the

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

potential for

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2},

respectively. In addition, close-coupled nuclear dynamics calculations that estimate the effect of this splitting on experimentally accessible quantities are presented. The splitting affects the collisional loss rate of magnetically trapped ultracold Rb and Cs atoms and the spectroscopic determination of the vibrational structure of

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

dimers. Agreement with the experimental collisional loss rates of Cs is found.

DOI: 10.1103/physreva.63.012517

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Hyperfine, rotational, and Zeeman structure of the lowest vibrational levels of the Rb87 2 (1) 3Σg+ state

T. Takekoshi, Christoph Strauß, Florian J. W. Lang +3 more

We present the results of an experimental and theoretical study of the electronically excited $(1){}^{3}{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ state of $^{87}\mathrm{Rb}$ ${}_{2}$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to ${v}^{\ensuremath{'}}=15$ using laser spectroscopy of ultracold Rb ${}_{2}$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47-GHz splitting into ${0}_{\mathrm{g}}^{\ensuremath{-}}$ and ${1}_{\mathrm{g}}$ components caused mainly by a strong second-order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe this structure to the first order using a simplified effective Hamiltonian.We present the results of an experimental and theoretical study of the electronically excited $(1){}^{3}{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ state of $^{87}\mathrm{Rb}$${}_{2}$ molecules. The vibrational energies are measured for deeply bound states from the bottom up to ${v}^{\ensuremath{'}}=15$ using laser spectroscopy of ultracold Rb${}_{2}$ Feshbach molecules. The spectrum of each vibrational state is dominated by a 47-GHz splitting into ${0}_{\mathrm{g}}^{\ensuremath{-}}$ and ${1}_{\mathrm{g}}$ components caused mainly by a strong second-order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe this structure to the first order using a simplified effective Hamiltonian.

arXiv:1104.3674Physical Review AJun 8, 201119 citations

We have calculated the splitting between the

{0}_{u}^{\ensuremath{-}}

and

{1}_{u}

components of the

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

state of

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

a{}^{3}{\ensuremath{\Sigma}}_{u}^{+}

potential for

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2},

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

dimers. Agreement with the experimental collisional loss rates of Cs is found.

{\mathrm{ea}}_{0}

at the equilibrium internuclear separation with excess negative charge on the potassium atom. For the $a{}^{3}{\ensuremath{\Sigma}}^{+}$ potential the dipole moment is an order of smaller magnitude (1 ${\mathrm{ea}}_{0}=8.47835{10}^{\ensuremath{-}30}\mathrm{Cm}).$ In addition, we calculate transition dipole moments between the two ground-state and excited-state potentials that dissociate to the

\mathrm{K}(4s)+\mathrm{Rb}(5p)

limits. Using this data we propose a way to produce singlet $X{}^{1}{\ensuremath{\Sigma}}^{+}$ KRb molecules by a two-photon Raman process starting from an ultracold mixture of doubly spin-polarized ground state K and Rb atoms. This Raman process is only allowed due to relativistic spin-orbit couplings and the absence of gerade-ungerade selection rules in heteronuclear dimers.

We present the results of an experimental and theoretical study of the electronically excited $(1){}^{3}{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ state of

^{87}\mathrm{Rb}

{}_{2}

molecules. The vibrational energies are measured for deeply bound states from the bottom up to ${v}^{\ensuremath{'}}=15$ using laser spectroscopy of ultracold Rb

{}_{2}

Feshbach molecules. The spectrum of each vibrational state is dominated by a 47-GHz splitting into ${0}_{\mathrm{g}}^{\ensuremath{-}}$ and

{1}_{\mathrm{g}}

components caused mainly by a strong second-order spin-orbit interaction. Our spectroscopy fully resolves the rotational, hyperfine, and Zeeman structure of the spectrum. We are able to describe this structure to the first order using a simplified effective Hamiltonian.