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 comprises only transitions involving electrons in the valence orbitals like , and , while transitions involving core electrons are neglected. Applying this formalism to the ground level of configuration , we restrict the sum to transitions implying the 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 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 are thus strongly related to the details of the atomic electronic structure. Those analytical results agree with our detailed electronic-structure calculations of the energy levels, Landé factors, transition probabilities, polarizabilities, and van der Waals coefficients, previously performed on erbium and dysprosium and presently performed on holmium. Our results show that, although the density of states decreases with increasing , the configuration interaction between , and is surprisingly stronger in erbium () than in holmium (), itself stronger than in dysprosium ().
- Received 13 April 2017
DOI:https://doi.org/10.1103/PhysRevA.95.062508
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