# Rovibrational dynamics of the strontium molecule in the A1Σu+, c3Πu, and a3Σu+ manifold from state-of-the-art ab initio calculations

**ABSTRACT** State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A1Σu+, c3Πu, and a3Σu+ manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X1Σg+ to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0u+ state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Knöckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]10.1140/epjd/e2011-20229-6. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A1Σu+←X1Σg+ transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the 1S0 + 3P1 dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.

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**ABSTRACT:**Weakly bound molecules have physical properties without atomic analogues, even as the bond length approaches dissociation. In particular, the internal symmetries of homonuclear diatomic molecules result in the formation of two-body superradiant and subradiant excited states. While superradiance has been demonstrated in a variety of systems, subradiance is more elusive due to the inherently weak interaction with the environment. Transition mechanisms that are strictly forbidden for atoms become allowed just below the dissociation asymptote due to new selection rules associated with the subradiant states. Here we directly probe deeply subradiant states in ultracold diatomic strontium molecules and characterize their properties near the intercombination atomic asymptote via optical spectroscopy of doubly-forbidden transitions with intrinsic quality factors exceeding 10^(13). This precision measurement of subradiance is made possible by tightly trapping the molecules in a state-insensitive optical lattice and achieving the longest molecule-light coherent interaction times. We find that two competing effects limit the lifetimes of the subradiant molecules, with different asymptotic behaviors. The first is radiative decay via magnetic-dipole and electric-quadrupole interactions. We prove that its rate increases quadratically with the bond length, confirming quantum mechanical predictions. The second is nonradiative decay through weak gyroscopic predissociation, with a rate proportional to the vibrational mode spacing and sensitive to short-range physics. This work bridges the gap between atomic and molecular metrology based on lattice-clock techniques, yielding some of the most accurate understanding of long-range interatomic interactions.Nature Physics 12/2014; 11:32–36. DOI:10.1038/nphys3182 · 20.60 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We present C6 homo- and heteroatomic dispersion coefficients for all closed-shell atoms of the periodic table based on dipole–dipole polarizabilities at imaginary frequencies calculated using our recent extension of the complex polarization propagator approach to the four-component relativistic Kohn–Sham approach. Lack of proper reference data bars definite conclusions as to which density functional shows the overall best performance, and we therefore call for state-of-the-art wave function-based correlated calculations of dispersion coefficients. Scalar relativistic effects are significant already for elements as light as zinc, whereas spin–orbit effects must be taken into account only for very heavy elements.Molecular Physics 10/2012; 110(19-20):1-7. DOI:10.1080/00268976.2012.709283 · 1.64 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The properties of the electronic ground state of the polar and paramagnetic europium-$S$-state-atom molecules have been investigated. Ab initio techniques have been applied to compute the potential energy curves for the europium-alkali-metal-atom, Eu$X$ ($X$=Li, Na, K, Rb, Cs), europium-alkaline-earth-metal-atom, Eu$Y$ ($Y$=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 $C_6$ 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.Physical Review A 09/2014; 90(2). DOI:10.1103/PhysRevA.90.022514 · 2.99 Impact Factor