Anisotropic optical trapping as a manifestation of the complex electronic structure of ultracold lanthanide atoms: The example of holmium
AbstractThe 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 6s,5d,6p, and 7s, while transitions involving 4f core electrons are neglected. Applying this formalism to the ground level of configuration 4fq6s2, we restrict the sum to transitions implying the 4fq6s6p 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 4fq6s6p 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 g factors, transition probabilities, polarizabilities, and van der Waals C6 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 4fq6s6p,4fq−15d6s2, and 4fq−15d26s is surprisingly stronger in erbium (q=12) than in holmium (q=11), itself stronger than in dysprosium (q=10).