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 configurationinteraction 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 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 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).

Theory of long-range interactions for Rydberg states attached to hyperfine-split cores

“…As an example, we computed the static polarizability for the s-Rydberg series with F T = 12. Reference [76] computed the frequency dependent polarizability for the Ho ground level configuration. From the discussion above, we expect that this series does not have a rapidly varying quantum defect.…”

Purely long-range polar molecules composed of identical lanthanide atoms

“…a from NIST database [74], b values calculated with Cowan code [75] as in Ref. [76] c from Ref. [77,78], d from Ref.…”

New opportunites for interactions and control with ultracold lanthanides

“…Because of the multi-valence-electron nature of lanthanides it is challenging to acquire an accurate knowledge of dipole polarizability. However, in the last years, tremendous progress has been made in calculating the atomic polarizability of various lanthanides; see e. g. [75][76][77][78][79]. In experiments, the scalar, vectorial, and tensorial dynamical polarizability at specific wavelengths have been measured for erbium [80], dysprosium [81][82][83][84], and thulium [79,85].…”