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Zeitschrift für Physik D Atoms Molecules and Clusters

Analytical interaction potentials of the long range alkali-metal dimers

M. Marinescu, A. Dalgarno

Published Sep 1, 1996• 48 citations
Publisher
DOI
10.1007/bf01426409

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Long-range potentials for two-species alkali-metal atoms

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We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}\ensuremath{-}{n}^{\ensuremath{'}}S,nS\ensuremath{-}{n}^{\ensuremath{'}}P,nS\ensuremath{-}{n}^{\ensuremath{'}}D,$ and $\mathrm{nP}\ensuremath{-}{n}^{\ensuremath{'}}P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{Rb}(6S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P){ }^{1,3}\ensuremath{\Sigma},\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P){ }^{1,3}\ensuremath{\Sigma},$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{N}\mathrm{a}(3D){ }^{1,3}\ensuremath{\Sigma}$ molecules to be the most attractive. The $\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P)$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P)$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{K}(4P)$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the ${1/R}^{6}$ van der Waals coefficient for the interaction between $\mathrm{Cs}(6S)$ and $\mathrm{Li}(2P)$ atoms.

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Casimir-Polder long-range interaction potentials between alkali-metal atoms

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A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the ${K}_{7}, {K}_{9},$ and ${K}_{11}$ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.

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A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the ${K}_{7}, {K}_{9},$ and ${K}_{11}$ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.

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Molecular spectroscopy and quantum control of homonuclear alkali dimers

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We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}\ensuremath{-}{n}^{\ensuremath{'}}S,nS\ensuremath{-}{n}^{\ensuremath{'}}P,nS\ensuremath{-}{n}^{\ensuremath{'}}D,$ and $\mathrm{nP}\ensuremath{-}{n}^{\ensuremath{'}}P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{Rb}(6S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P){ }^{1,3}\ensuremath{\Sigma},\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P){ }^{1,3}\ensuremath{\Sigma},$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{N}\mathrm{a}(3D){ }^{1,3}\ensuremath{\Sigma}$ molecules to be the most attractive. The $\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P)$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P)$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{K}(4P)$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the 1/R6{1/R}^{6}1/R6 van der Waals coefficient for the interaction between Cs(6S)\mathrm{Cs}(6S)Cs(6S) and Li(2P)\mathrm{Li}(2P)Li(2P) atoms.
A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the K7,K9,{K}_{7}, {K}_{9},K7​,K9​, and K11{K}_{11}K11​ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.
A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the K7,K9,{K}_{7}, {K}_{9},K7​,K9​, and K11{K}_{11}K11​ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.