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Physical Review A

Ab initiostudy of permanent electric dipole moment and radiative lifetimes of alkaline-earth-metal--Li molecules

Geetha Gopakumar, Minori Abe, Masatoshi Kajita, Masahiko Hada

Published Dec 28, 2011• 41 citations
Publisher

Abstract

We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the ${}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}$ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: ${}^{24}$Mg${}^{7}$Li, ${}^{40}$Ca${}^{7}$Li, ${}^{88}$Sr${}^{7}$Li, and ${}^{138}$Ba${}^{7}$Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the $\ensuremath{\nu}$ $=$ 0 state (${}^{24}$Mg${}^{6}$Li: 22 s, ${}^{40}$Ca${}^{6}$Li: 39 s, ${}^{88}$Sr${}^{6}$Li: 380 s, and ${}^{138}$Ba${}^{6}$Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10$%$.

DOI
10.1103/physreva.84.062514

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We calculate permanent electric dipole moments (PDMs), as well as spontaneous and black body lifetimes, of alkaline-earth-metal--Li (AEM-Li) ultracold polar molecules to study anisotropic long-range dipole-dipole interactions in a single quantum state. We obtain potential energy curves for the 2\ensuremathΣ{}^{2}\phantom{\rule{-0.16em}{0ex}}\ensuremath{\Sigma}2\ensuremathΣ ground state of MgLi, CaLi, SrLi, and BaLi molecules at the coupled cluster singles and doubles with partial triples [CCSD(T)] level of electron correlation. Calculated spectroscopic constants for the isotopes: 24{}^{24}24Mg7{}^{7}7Li, 40{}^{40}40Ca7{}^{7}7Li, 88{}^{88}88Sr7{}^{7}7Li, and 138{}^{138}138Ba7{}^{7}7Li, show good agreement with available theoretical and experimental results. We obtain PDM curves using finite field perturbation theory at the CCSD(T) level. We find that AEM-Li molecules have moderate values of PDM at the equilibrium bond distance (MgLi: 0.90 D, CaLi: 1.15 D, SrLi: 0.33 D, and BaLi: --0.42 D) and hence might be suitable candidates for the proposed study in a single quantum state. Radiative lifetime calculations of the \ensuremathν\ensuremath{\nu}\ensuremathν === 0 state (24{}^{24}24Mg6{}^{6}6Li: 22 s, 40{}^{40}40Ca6{}^{6}6Li: 39 s, 88{}^{88}88Sr6{}^{6}6Li: 380 s, and 138{}^{138}138Ba6{}^{6}6Li: 988 s) are found to be longer than the typical time scale associated with ultracold experiments with these molecules. The uncertainty in the lifetime calculations are estimated to be less than 10%.
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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.
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We investigate the lifetimes of vibrational states of diatomic alkali-alkaline-earth cations to determine their suitability for ultracold experiments where long decoherence time and controllability by an external electric field are desirable. The potential energy and permanent dipole moment curves for the ground electronic states of LiBe+, LiMg+, NaBe+, and NaMg+ are obtained using the coupled cluster with singles doubles and triples and multireference configuration interaction methods in combination with large all-electron cc-pCVQZ and aug-cc-pCV5Z basis sets. The energies and wave functions of all vibrational states are obtained by solving the Schrödinger equation for nuclei with the B-spline basis set method. To predict the lifetimes of vibrational states, the transition dipole moments, as well as the Einstein coefficients describing spontaneous emission, and the stimulated absorption and emission induced by black body radiation are calculated. Surprisingly, in all studied ions, the lifetimes of the highest excited vibrational states are similar to the lifetimes of the ground vibrational states indicating that highly vibrationally excited ions could be useful for the ultracold experiments requiring long decoherence time.
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The properties of the electronic ground state of the polar and paramagnetic europium--S-state-atomS\text{-state-atom}S-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium--alkali-metal-atom, EuX(X=Li,Na,K,Rb,Cs)\mathrm{Eu}X(X=\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Rb},\mathrm{Cs})EuX(X=Li,Na,K,Rb,Cs), europium--alkaline-earth-metal-atom, EuY(Y=Be,Mg,Ca,Sr,Ba)\mathrm{Eu}Y(Y=\mathrm{Be},\mathrm{Mg},\mathrm{Ca},\mathrm{Sr},\mathrm{Ba})EuY(Y=Be,Mg,Ca,Sr,Ba), and europium-ytterbium, EuYb, molecules in the Born-Oppenheimer approximation for the high-spin electronic ground state. The spin restricted open-shell coupled cluster method restricted to single, double, and noniterative triple excitations, RCCSD(T), was employed and the scalar relativistic effects within the small-core energy-consistent pseudopotentials were included. The permanent electric dipole moments and static electric dipole polarizabilities were computed. The leading long-range coefficients describing the dispersion interaction between atoms at large internuclear distances C6{C}_{6}C6​ are also reported. The EuK, EuRb, and EuCs molecules are examples of species possessing both large electric and magnetic dipole moments making them potentially interesting candidates for ultracold many-body quantum simulations when confined in an optical lattice in combined electric and magnetic fields.