Anisotropic optical trapping as a manifestation of the complex electronic structure of ultracold lanthanide atoms: the example of holmium

Abstract

The efficiency of optical trapping is determined by the atomic dynamic dipole polarizability, whose real and imaginary parts are associated with the potential energy and photon-scattering rate respectively. In this article we develop a formalism to calculate analytically the real and imaginary parts of the scalar, vector and tensor polarizabilities of lanthanide atoms. We assume that the sum-over-state formula only comprises transitions involving electrons in the valence orbitals like $6s$, $5d$, $6p$ or $7s$, while transitions involving $4f$ core electrons are neglected. Applying this formalism to the ground level of configuration $4f^{q}6s^2$, we restrict the sum to transitions implying the $4f^{q}6s6p$ configuration, which yields polarizabilities depending on two parameters: an effective transition energy and an effective transition dipole moment. Then, by introducing configuration-interaction mixing between $4f^{q}6s6p$ and other configurations, we demonstrate that the imaginary part of the scalar, vector and tensor polarizabilities is very sensitive to configuration-interaction coefficients, whereas the real part is not. The magnitude and anisotropy of the photon-scattering rate is thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of energy levels, Landé $g$-factors, transition probabilities, polarizabilities and van der Waals $C_6$ coefficients, previously performed on erbium and dysprosium, and presently performed on holmium. Our results show that, although the density of states decreases with increasing $q$, the configuration interaction between $4f^{q}6s6p$, $4f^{q-1}5d6s^2$ and $4f^{q-1}5d^{2}6s$ is surprisingly stronger in erbium ($q=12$), than in holmium ($q=11$), itself stronger than in dysprosium ($q=10$).

18 pages, 6 figures

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Cited by in corpus (18)

• Tools for quantum simulation with ultracold atoms in optical lattices
• Dipolar physics: A review of experiments with magnetic quantum gases
• Accurate Determination of the Dynamical Polarizability of Dysprosium
• Anisotropic polarizability of erbium atoms
• Study of the inter-species interactions in an ultracold dipolar mixture
• Dysprosium dipolar Bose-Einstein condensate with broad Feshbach resonances
• Anisotropic light-shift and magic-polarization of the intercombination line of Dysprosium atoms in a far-detuned dipole trap
• Theory of long range interactions for Rydberg states attached to hyperfine split cores
• Observation of a narrow inner-shell orbital transition in atomic erbium at 1299 nm
• Optical Tweezer Arrays of Erbium Atoms
• Ultracold rare-earth magnetic atoms with an electric dipole moment
• Characterizing the temperature dependence of Fano-Feshbach resonances of Ultracold Polarized Thulium
• Measurement of the dynamic polarizability of Dy atoms near the 626-nm intercombination line
• Hubbard parameters for programmable tweezer arrays
• New opportunites for interactions and control with ultracold lanthanides
• Purely long-range polar molecules composed of identical lanthanide atoms
• Dissipationless tune-out trapping for a lanthanide-alkali quantum gas mixture
• Van der Waals coefficients for interactions of dysprosium and erbium atoms with alkali-metal and alkaline-earth-metal atoms