Atomic clocks based on an ${\mathrm{Al}}^{+}$ ion sympathetically cooled by a laser-cooled alkaline-earth-metal ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge-transfer dynamics of an ${\mathrm{Al}}^{+}$ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the ${(\mathrm{Al}+\mathrm{Rb})}^{+}$ and ${(\mathrm{Al}+\mathrm{Sr})}^{+}$ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge-transfer dynamics. Scattering of an ${\mathrm{Al}}^{+}$ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an ${\mathrm{Al}}^{+}$ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.
Atomic clocks based on an Al+ ion sympathetically cooled by a laser-cooled alkaline-earth-metal ion have achieved unprecedented accuracy. Here, we investigate theoretically interactions and charge-transfer dynamics of an Al+ ion immersed in an ultracold gas of Rb and Sr atoms. We calculate potential energy curves and transition electric dipole moments for the (Al+Rb)+ and (Al+Sr)+ ion-atom systems using coupled cluster and multireference configuration interaction methods with scalar relativistic effects included within the small-core energy-consistent pseudopotentials in Rb and Sr atoms. The long-range interaction coefficients are also reported. We use the electronic structure data to investigate cold collisions and charge-transfer dynamics. Scattering of an Al+ ion with alkali-metal or alkaline-earth-metal atom is governed by one potential energy curve whereas charge transfer can lead to several electronic states mixed by the relativistic spin-orbit coupling. We examine the branching ratios resulting from the interplay of the short- and long-range effects, as well as the prospects for the laser-field control and formation of molecular ions. We propose to employ the atomic clock transition in an Al+ ion to monitor ion-atom scattering dynamics via quantum logic spectroscopy. The presented results pave the way for the application of atomic ions other than alkali-metal and alkaline-earth-metal ones in the field of cold hybrid ion-atom experiments.
Abstract Molecular ions formed in cold hybrid ion–atom experiments may find interesting applications ranging from precision measurements to controlled chemical reactions. Here, we investigate the electronic structure of the Sr 2 + molecular ion, which may be produced by photoassociation of laser-cooled Sr+ ions immersed in an ultracold gas of Sr atoms or by ionization of ultracold Sr2 molecules. Using ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones with small-core relativistic energy-consistent pseudopotentials and large Gaussian basis sets, we calculate potential energy curves for the ground and 41 excited electronic states, and electric dipole transition moments between them. We show that alkaline-earth molecular ions, despite their apparently simple structure with only three valence electrons, are challenging for state-of-the-art quantum chemistry methods due to their multireference nature and high density of states. Finally, we calculate and analyze Franck–Condon factors governing the photoionization of ground-state Sr2 molecules into Σ u + 2 and Σ g + 2 states of Sr 2 + molecular ions. The present results may be useful for studying and guiding the formation and spectroscopy of cold Sr 2 + molecular ions.
Abstract Molecular ions formed in cold hybrid ion-atom experiments may find interesting applications ranging from precision measurements to controlled chemical reactions. Here, we investigate electronic structure of the Sr2 + molecular ion, which may be produced by photoassociation of laser-cooled Sr+ ions immersed into an ultracold gas of Sr atoms or by ionization of ultracold Sr2 molecules. Using ab initio electronic structure methods, such as the coupled cluster and configuration interaction ones with small-core relativistic energy-consistent pseudopotentials and large Gaussian basis sets, we calculate potential energy curves for the ground and 41 excited electronic states, and electric dipole transition moments between them. We show that alkaline-earth molecular ions despite of their apparently simple structure with three valence electrons only are challenging for state-of-the-art quantum chemistry methods due to their multireference nature and high density of states. Finally, we calculate and analyze Franck-Condon factors governing the photoionization of ground-state Sr2 molecules into 2Σu + and 2Σg + states of Sr2 + molecular ions. The present results may be useful for studying and guiding formation and spectroscopy of cold Sr2 + molecular ions.
) with alkali-metal (Li, Na, K, Rb, Cs) and alkaline-earth-metal (Mg, Ca, Sr, Ba) atoms. State-of-the-art ab initio techniques are applied to compute the potential energy surfaces (PESs) for these systems. The coupled cluster method restricted to single, double, and noniterative triple excitations, CCSD(T), is employed and the scalar relativistic effects in heavier metal atoms are modeled within the small-core energy-consistent pseudopotentials. The leading long-range isotropic and anisotropic induction and dispersion interaction coefficients are obtained within the perturbation theory. The PESs are characterized in detail and their universal similarities typical for systems dominated by the induction interaction are discussed. The two-dimensional PESs are provided for selected systems and can be employed in scattering calculations. The possible channels of chemical reactions and their control are analyzed based on the energetics of the reactants. The present study of the electronic structure is the first step towards the evaluation of prospects for sympathetic cooling and controlled chemistry of linear polyatomic ions with ultracold 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.
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.
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.