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arXiv:1104.3015 · Physical Chemistry Chemical Physics

Formation of ultracold SrYb molecules in an optical lattice by photoassociation spectroscopy: theoretical prospects

Michał Tomza, Filip Pawłowski, Małgorzata Jeziorska, Christiane P. Koch, Robert Moszyński

Published Jan 1, 2011• 41 citations
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Abstract

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.

DOI
10.1039/c1cp21196j

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State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the SrYb molecule in the Born-Oppenheimer approximation for the electronic ground state and the first fifteen excited singlet and triplet states. All the excited state potential energy curves were computed using the equation of motion approach within the coupled-cluster singles and doubles framework and large basis-sets, while the ground state potential was computed using the coupled cluster method with single, double, and noniterative triple excitations. The leading long-range coefficients describing the dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. The electronic structure data were employed to investigate the possibility of forming deeply bound ultracold SrYb molecules in an optical lattice in a photoassociation experiment using continuous-wave lasers. Photoassociation near the intercombination line transition of atomic strontium into the vibrational levels of the strongly spin-orbit mixed b(3)Σ(+), a(3)Π, A(1)Π, and C(1)Π states with subsequent efficient stabilization into the v'' = 1 vibrational level of the electronic ground state is proposed. Ground state SrYb molecules can be accumulated by making use of collisional decay from v'' = 1 to v'' = 0. Alternatively, photoassociation and stabilization to v'' = 0 can proceed via stimulated Raman adiabatic passage provided that the trapping frequency of the optical lattice is large enough and phase coherence between the pulses can be maintained over at least tens of microseconds.
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This paper discusses the formation of ultracold YbAg molecules via photoassociation, following the proposal of using YbAg as a promising molecular candidate for electron electric dipole moment experiments [M. Verma et al. Phys. Rev. Lett. 125, 153201 (2020)]. Our study utilizes high-level ab initio calculations, encompassing both multireference configuration interaction, relativistic Fock-space coupled cluster, and Kramers-restricted configuration interaction methods, to investigate the electronic structures including potential energy curves, spectroscopic constant, vibrational energy levels, and associated transition dipole moment and Franck-Condon factors for 28 electronic states. By choosing (5)($\mathrm{\ensuremath{\Omega}}=3/2$) as the intermediate state, we discuss the feasibility of forming ultracold YbAg molecules through stimulated Raman adiabatic passage method.
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Alkali hydride molecules are polar, exhibiting large ground-state dipole moments. As ultracold sources of alkali atoms, as well as hydrogen, have been created in the laboratory, we explore theoretically the feasibility of forming such molecules from a mixture of the ultracold atomic gases, employing various photoassociation schemes. In this work we use lithium and sodium hydride as benchmark systems to calculate molecule formation rates through stimulated one-photon radiative association directly from the continuum as well as two-photon stimulated radiative association (Raman transfer) and excitation to bound levels of an excited state followed by spontaneous emission to the ground state. Using accurate molecular potential energy curves and dipole transition moments and with laser intensities and MOT densities that are easily attainable experimentally, we have found that substantial molecule formation rates can be realized even after the effect of back-stimulation has been accounted for. We examine the spontaneous emission cascade which takes place from the upper vibrational levels of the singlet ground state on a time scale of milliseconds. Because photon emission in the cascade process does not contribute to trap loss, a sizable population of molecules in the lowest vibrational level can be achieved. The triplet ground electronic state is of particular interest for experimental efforts since, although it has never been observed experimentally, molecular structure calculations of the a3Σ+ state for LiH and NaH predict a small van der Waals attraction, with a potential energy well so shallow that it can support only one bound rotational-vibrational level. Any molecule formed in the triplet ground state would then be immediately in the lowest and most stable level of that state and would be quite long-lived, unlike molecules in high vibrational levels which have significantly shorter lifetimes. As an analysis of our method of calculating molecule formation rates, we investigate more thoroughly the two-photon stimulated photoassociation process by employing the exact treatment of Dalgarno & Lewis to solve the Raman scattering problem. ^