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arXiv:2103.13829 · Physical Review A

Long-range additive and nonadditive potentials in a hybrid system: Ground-state atom, excited-state atom, and ion

Pei-Gen Yan, Li-Yan Tang, Zong-Chao Yan, J. F. Babb

Published Aug 10, 2021• 4 citations
arXivHTMLPDF

Abstract

We report a theoretical study on the long-range additive and nonadditive potentials for a three-body hybrid atom-atom-ion system composed of one ground-$S$-state Li atom, one excited-$P$-state Li atom, and one ground-$S$-state ${\mathrm{Li}}^{+}$ ion, $\mathrm{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}S)\text{\ensuremath{-}}\mathrm{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}P)\text{\ensuremath{-}}{\mathrm{Li}}^{+}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S$). The interaction coefficients are evaluated with highly accurate wave functions calculated variationally in Hylleraas coordinates. For this hybrid system the three-body nonadditive interactions (appearing in second order) induced by the energy degeneracy and enhanced by the induction effect of the ${\mathrm{Li}}^{+}$ ion through the internal electric field can be strong and even stronger than the two-body additive interactions at the same order. We find that for particular geometries the two-body additive interactions of the system sum to zero, leaving only three-body nonadditive interactions, thus making the present system potentially a platform to explore quantum three-body effects. We also extract by first principles the leading coefficients of the long-range electrostatic, induction, and dispersion energies of ${\text{Li}}_{2}{}^{+}$ electronic states correlating to ${\text{Li}}^{+}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\ensuremath{-}\text{Li}(2{\phantom{\rule{0.16em}{0ex}}}^{2}P)$. The results should be especially valuable for the exploration of schemes to create trimers with ultracold atoms and ions in optical lattices.

DOI
10.1103/physreva.104.022807

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We theoretically characterize interactions, energetics, and chemical reaction paths in ionic two-body and three-body systems of alkali-metal and alkaline-earth-metal atoms in the context of modern experiments with cold hybrid ion-atom mixtures. Using ab initio techniques of quantum chemistry such as the coupled-cluster method, we calculate ground-state electronic properties of all diatomic AB+A{B}^{+}AB+ and most of the triatomic A2B+{A}_{2}{B}^{+}A2​B+ molecular ions consisting of Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, and Yb atoms. Different geometries and wave-function symmetries of the ground state are found for different classes of molecular ions. We analyze intermolecular interactions in the investigated systems including additive two-body and nonadditive three-body ones. As an example we provide two-dimensional interaction potential-energy surfaces for KRb++K{\mathrm{KRb}}^{+}+\mathrm{K}KRb++K and Rb++Sr2{\mathrm{Rb}}^{+}+{\mathrm{Sr}}_{2}Rb++Sr2​ mixtures. We identify possible channels of chemical reactions based on the energetics of the reactants. The present results may be useful for investigating controlled chemical reactions and other applications of molecular ions formed in cold hybrid ion-atom systems.
Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a nonzero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nondiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb((2)S) atom with CO((3)Π), OH((2)Π), NH((1)Δ), and CH((2)Π) and of the ground state Li((2)S) atom with CH((2)Π).
Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca+^++, Ba+^++, Sr+^++, and Ra+^++ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation RRR. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus RRR are given among all the considered atoms and ions.