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arXiv:cond-mat/0305215 · Physical Review A

Ab initiocalculation of the KRb dipole moments

Svetlana Kotochigova, Paul S. Julienne, Eite Tiesinga

Published Aug 11, 2003• 83 citations
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Abstract

The relativistic configuration interaction valence-bond method has been used to calculate permanent and transition electric dipole moments of the KRb heteronuclear molecule as a function of internuclear separation. The permanent dipole moment of the ground-state $X{}^{1}{\ensuremath{\Sigma}}^{+}$ potential is found to be 0.30(2) ${\mathrm{ea}}_{0}$ 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.

DOI
10.1103/physreva.68.022501

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The relativistic configuration interaction valence-bond method has been used to calculate permanent and transition electric dipole moments of the KRb heteronuclear molecule as a function of internuclear separation. The permanent dipole moment of the ground-state X1\ensuremathΣ+X{}^{1}{\ensuremath{\Sigma}}^{+}X1\ensuremathΣ+ potential is found to be 0.30(2) ea0{\mathrm{ea}}_{0}ea0​ at the equilibrium internuclear separation with excess negative charge on the potassium atom. For the a3\ensuremathΣ+a{}^{3}{\ensuremath{\Sigma}}^{+}a3\ensuremathΣ+ potential the dipole moment is an order of smaller magnitude (1 ea0=8.4783510\ensuremath−30Cm).{\mathrm{ea}}_{0}=8.47835{10}^{\ensuremath{-}30}\mathrm{Cm}).ea0​=8.4783510\ensuremath−30Cm). In addition, we calculate transition dipole moments between the two ground-state and excited-state potentials that dissociate to the K(4s)+Rb(5p)\mathrm{K}(4s)+\mathrm{Rb}(5p)K(4s)+Rb(5p) limits. Using this data we propose a way to produce singlet X1\ensuremathΣ+X{}^{1}{\ensuremath{\Sigma}}^{+}X1\ensuremathΣ+ 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.
Heteronuclear dimers are of significant interest to experiments seeking to exploit ultracold polar molecules in a number of novel ways, including precision measurement, quantum computing and quantum simulation. We calculate highly accurate Born–Oppenheimer total energies and electric dipole moments as a function of internuclear separation for two such dimers, LiSr and KRb. We apply fully correlated, high-accuracy quantum Monte Carlo methods for evaluating these molecular properties in a many-body framework. We use small-core effective potentials combined with multi-reference Slater–Jastrow trial wave functions to provide accurate nodes for the fixed-node diffusion Monte Carlo method. For reference and comparison, we calculate the same properties with Hartree–Fock and with restricted Configuration Interaction methods, and carefully assess the impact of the recovered many-body correlations on the calculated quantities. For LiSr, we find a highly non-linear dipole moment curve, which may make this molecule’s dipole moment tunable through vibrational state control.
We apply the relativistic configuration-interaction valence-bond method to calculate various characteristics of the alkali-metal RbCs dimer. These include the electronic potentials and transition dipole moments between the ground and first excited states and permanent dipole moments of the X 1sigma+ and a 3sigma+ states of the ground configuration. In addition, we estimate the lifetime of the rovibrational levels of the X state due to blackbody radiation. These data can help experimentalists to optimize photoassociative formation of ultracold RbCs molecules and their longevity in a trap or in an optical lattice. Extended basis sets, constructed from Dirac-Fock and Sturm's orbitals, have been used to ensure convergence of our calculations. We compare our data with other theoretical and experimental results when they were available.
This paper deals with the electronic structure of RbSr, a molecule possessing both a magnetic dipole moment and an electric dipole moment in its own frame, allowing its manipulation with external fields. Two complementary ab initio approaches are used for the ground and lowest excited states: first, an approach relying on optimized effective core potentials with core polarization potentials based on a full configuration interaction involving three valence electrons and second, an approach using a small-size effective core potential with 19 correlated electrons in the framework of coupled-cluster theory. We have found excellent agreement between these two approaches for the ground-state properties including the permanent dipole moment. We have focused on studies of excited states correlated to the two lowest asymptotes Rb(5p2P)\mathrm{Rb}(5p{\phantom{\rule{0.16em}{0ex}}}^{2}P)Rb(5p2P)+Sr(5s21S)+\mathrm{Sr}(5{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}S)+Sr(5s21S) and Rb(5s2S)\mathrm{Rb}(5s{\phantom{\rule{0.16em}{0ex}}}^{2}S)Rb(5s2S)+Sr(5s5p3P)+\mathrm{Sr}(5s5p{\phantom{\rule{0.16em}{0ex}}}^{3}P)+Sr(5s5p3P) relevant for ongoing experiments on ultracold quantum degenerate gases. We also present approximate potential curves including spin-orbit interaction based on atomic spin-orbit constants. These potential curves are an excellent starting point for experimental studies of molecular structure of RbSr using high-resolution spectroscopy.
In this study, we investigate the structure of the polar alkali-metal-atom--strontium diatomic molecules as possible candidates for the realization of samples of ultracold polar molecular species not yet investigated experimentally. Using a quantum chemistry approach based on effective core potentials and core polarization potentials, we model these systems as effective three-valence-electron systems, allowing for calculation of electronic properties with full configuration interaction. The potential curve and the permanent dipole moment of the ${}^{2}{\ensuremath{\Sigma}}^{+}$ ground state are determined as functions of the internuclear distance for LiSr, NaSr, KSr, RbSr, and CsSr molecules. These molecules are found to exhibit a significant permanent dipole moment, though smaller than those of the alkali-metal-atom--Rb molecules.
We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule (52Cr^{52}\mathrm{Cr}52Cr87Rb^{87}\mathrm{Rb}87Rb), and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient (C6=1770{C}_{6}=1770C6​=1770 a.u.) has an expected error of 33%3. The ground state ${}^{6}{\ensuremath{\Sigma}}^{+}$ molecule at its equilibrium separation has a permanent electric dipole moment of de(Re=3.34A˚)=2.90D{d}_{e}({R}_{e}=3.34\AA{})=2.90 Dde​(Re​=3.34A˚)=2.90D. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of 102{10}^{2}102--103{10}^{3}103.
The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.