Anisotropic optical trapping of ultracold erbium atoms

Abstract

Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose-condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and transition dipole moments from ground-state erbium, which are computed using the Racah-Slater least-square fitting procedure provided by the Cowan codes. This allows us to predict 9 unobserved odd-parity energy levels of total angular momentum J=5, 6 and 7, in the range 25000-31000 cm-1 above the ground state. Regarding the trapping potential, we find that ground-state erbium essentially behaves like a spherically-symmetric atom, in spite of its large electronic angular momentum. We also find a mostly isotropic van der Waals interaction between two ground-state erbium atoms, characterized by a coefficient C_6^{iso}=1760 a.u.. On the contrary, the photon-scattering rate shows a pronounced anisotropy, since it strongly depends on the polarization of the trapping light.Comment: 15 pages, 5 figure

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

“…As discussed in Ref. [45], the agreement on energy is very good. As for transition probabilities, the overall agreement is satisfactory, even if the theoretical transition probabilities and weights are globally smaller than the experimental ones.…”

“…stand for theoretical (see Refs. [45,46] and subsection III C) and experimental [53][54][55] transition energies and transition probabilities respectively. The columns "Eq.…”

“…whose natural linewidth γ βJ is negligible compared to the photonscattering rate induced by the electromagnetic field [44,45]. In practice, this may concern excited levels of the lowest configuration 4f q 6s 2 or the levels…”

“…In our previous work on erbium [45], we described the odd-parity levels with the configurations 4f 12 6s6p, 4f 11 5d6s 2 and 4f 11 5d 2 6s, which is likely to yield a reliable calculation of the weights w…”

Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules

“…(13) and (14)), obtained by considering complex energies in the usual expression of the DDP (see our previous works on other diatomics [37,38] and lanthanide atoms [48][49][50]). Equation (14) is even with respect to ω, and non-zero for ω = 0.…”