Vibronic transitions in the alkali-metal (Li, Na, K, Rb) – alkaline-earth-metal (Ca, Sr) series: A systematic analysis of de-excitation mechanisms based on the graphical mapping of Frank-Condon integrals
Johann Valentin Pototschnig, Ralf Meyer, Andreas W. Hauser, Wolfgang Ernst
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. After forming weakly bound molecules from atoms in cold collisions, the preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. Accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. This paper is dedicated to the vibrational analysis of potentially relevant electronically excited states in the alkali-metal (Li, Na, K, Rb)-- alkaline-earth metal (Ca,Sr) diatomic series. Graphical maps of Frank-Condon overlap integrals are presented for all molecules of the group. By comparison to overlap graphics produced for idealized potential surfaces, we judge the usability of the selected states for future experiments on laser-enhanced molecular formation from mixtures of quantum degenerate gases.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. After forming weakly bound molecules from atoms in cold collisions, the preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. Accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. This paper is dedicated to the vibrational analysis of potentially relevant electronically excited states in the alkali-metal (Li, Na, K, Rb)-- alkaline-earth metal (Ca,Sr) diatomic series. Graphical maps of Frank-Condon overlap integrals are presented for all molecules of the group. By comparison to overlap graphics produced for idealized potential surfaces, we judge the usability of the selected states for future experiments on laser-enhanced molecular formation from mixtures of quantum degenerate gases.
Research on ultracold molecules has seen a growing interest recently in the context of high-resolution spectroscopy and quantum computation. The preparation of molecules in low vibrational levels of the ground state is experimentally challenging, and typically achieved by population transfer using excited electronic states. On the theoretical side, highly accurate potential energy surfaces are needed for a correct description of processes such as the coherent de-excitation from the highest and therefore weakly bound vibrational levels in the electronic ground state via couplings to electronically excited states. Particularly problematic is the correct description of potential features at large intermolecular distances. Franck-Condon overlap integrals for nuclear wavefunctions in barely bound vibrational states are extremely sensitive to inaccuracies of the potential at long range. In this study, we compare the predictions of common, wavefunction-based ab initio techniques for a known de-excitation mechanism in alkali-alkaline earth dimers. It is the aim to analyze the predictive power of these methods for a preliminary evaluation of potential cooling mechanisms in heteronuclear open shell systems which offer the experimentalist an electric as well as a magnetic handle for manipulation. The series of X-Sr molecules, with X = Li, Na, K and Rb, has been chosen for a direct comparison. Quantum degenerate mixtures of Rb and Sr have already been produced,\footnote{B. Pasquiou, A. Bayerle, S. M. Tzanova, S. Stellmer, J. Szczepkowski, M. Parigger, R. Grimm, and F. Schreck, Phys. Rev. A, 2013, 88, 023601} making this combination very promising for the production of ultracold molecules.
Studies of anions are inherently more challenging than investigations of neutrals and cations because of the diffuse and weakly bound character of an anionic electron. Here, we present a comprehensive computational examination of ground-state diatomic molecular anions composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 21 alkali-metal diatomic anions in the X2Σ+ electronic state and 36 alkali-metal--alkaline-earth-metal diatomic anions in the X1Σ+ electronic state. The calculations employ a hierarchy of the coupled cluster methods, combined with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials for heavier elements. We compute potential energy curves, permanent electric dipole moments, and static polarizabilities, and we assess convergence and uncertainties of our results. Additionally, using the multireference configuration interaction and equation-of-motion electron-attachment coupled cluster methods, we investigate excited electronic states of alkali-metal molecular anions, including valence-bound and dipole-bound states. We predict crossings between ground neutral and excited anionic states, which may enhance resonant electron attachment and subsequent anion dissociation. This finding may be relevant for experiments with mixtures of ultracold ground-state alkali-metal molecules and Rydberg atoms.
Ultracold diatomic molecules find application in quantum studies ranging from controlled chemistry and precision measurement physics to quantum many-body simulation and potentially quantum computing. Accurate knowledge of molecular properties is required to guide and explain ongoing experiments. Here, in an extensive and comparative study, we theoretically investigate the electronic properties of the ground-state diatomic molecules composed of alkali-metal (Li, Na, K, Rb, Cs, Fr) and alkaline-earth-metal (Be, Mg, Ca, Sr, Ba, Ra) atoms. We study 78 heteronuclear and homonuclear diatomic combinations, including 21 alkali-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ and ${a}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic states, 36 alkali-metal--alkaline-earth-metal molecules in the ${X}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state, and 21 alkaline-earth-metal molecules in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+}$ electronic state. We calculate potential energy curves, permanent electric dipole moments, and polarizabilities using the hierarchy of coupled-cluster methods up to CCSDTQ with large Gaussian basis sets and small-core relativistic energy-consistent pseudopotentials. We collect and analyze corresponding spectroscopic constants. We estimate computational uncertainties and compare the present values with previous experimental and theoretical data to establish a different theoretical benchmark. The presented results should be useful for further application of the studied molecules in modern ultracold physics and chemistry experiments.
Abstract Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr+ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 11Σ+ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f 00 = 0.987, f 11 = 0.959 and f 22 = 0.919 were obtained for the 11Π (v′ = 0, 1, 2)→ 11Σ+ (v = 0, 1, 2) transition making the BeFr+ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.
The experimental field of ultracold ion-atom mixtures including an alkali-metal atom and an alkaline-earth-metal ion as well as of homonuclear alkali dimers has paved the way for creating and manipulating the ultracold molecules. The present paper is focused on a study of molecules such us francium dimer and a comparative spectroscopic investigation of the cationic systems Fr–(Ca +, Sr +, Ba + ). We adopt a computational scheme without spin–orbit coupling reposed on the full configuration interaction and semi-empirical pseudo-potential theory of the atomic cores Fr +, Ca 2+, Sr 2+, and Ba 2+ with extended and optimized basis sets. We have determined the adiabatic potentials with their relative spectroscopic constants, the electric dipole moments and the vibrational levels spacings for the 1,3 Σ u,g + and 1,3 Σ + electronic states for Fr 2 and Fr–AEM +, respectively, correlated toward {Fr(7s) + Fr(7s, 7p, 6d, 8s, 8p)}, {Ca(4s 2, 4s4p, 4s3d), Sr(5s 2, 5s5p, 5s4d), Ba(6s 2, 6s6p, 6s5d) + Fr + }, and {Ca + (4s, 3d), Sr + (5s, 4d), Ba + (6s, 5d) + Fr(7s, 7p)}. The accuracy and reliability of the current results are discussed by comparing with theoretical data available in the literature. The occurrence of some avoided crossings between the neighboring electronic states is leading to a charge or excitation transfer for atom–ion collisions in the diverse charge or excited states. The Σ + –Σ + transitions are determined in order to evaluate the future radiative lifetimes of vibrational states serving the direct laser cooling.
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+ and most of the triatomic A2B+ 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 and 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.