Optical trapping of ultracold dysprosium atoms: transition probabilities, dynamic dipole polarizabilities and van der WaalsC₆coefficients

Abstract

Abstract. The efficiency of optical trapping of ultracold atoms depend on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited level. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the C 6 coefficients characterizing the van der Waals interaction between two dysprosium atoms in the two lowest levels. We have computed the energies of excited states and the transition probabilities appearing in the sums, using a combination of ab initio and least-square-fitting techniques provided by the Cowan codes and extended in our group. Regarding the real part of the polarizability, for field frequencies far from atomic resonances, the vector and tensor contributions are two-order-of-magnitude smaller than the scalar contribution, whereas for the imaginary part, the vector and tensor contributions represent a noticeable fraction of the scalar contribution. This offers the possibility to control the decoherence and trap losses due to spontaneous emission.

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

“…Such conclusions are also valid for any level belonging to the lowest configuration 4f q 6s 2 , as shown in our previous articles (see Ref. [46] and in subsection III C).…”

“…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.…”

“…(40), one usually finds 2.1 to 2.4 × 10 8 s −1 . Among those transitions, some are certainly not due to 6s-6p, but rather to 4f -5d excitation; however they are so weak that they will not affect the calculation of w 2 6s for dysprosium [46], or 4f 10 5d 2 6s for holmium (see section III). So for erbium, the "experimental" weights, given by Eq.…”

“…Beyond trapping itself, the real part of the vector and tensor DDPs are also necessary to determine the Ramancoupling strengths between different Zeeman sublevels, which was proposed for the implementation of synthetic gauge fields [17,18]. In our previous works on Er [45] and Dy [46], we have shown that, far from resonant fre-quencies, the ac-Stark shift only weakly depends on the field polarization and atomic Zeeman sublevel, despite the absence of spherical symmetry in the 4f -electron wave functions. We have unveiled the inverse situation for photon-scattering, as the imaginary part of the vector and tensor DDPs represent significant fractions of the scalar one.…”

“…The DDPs and C 6 coefficients are calculated using the sum formula involving transition energies and transition dipole moments extracted from our computed transition probabilities. Following our previous work [45][46][47][48], those quantities are calculated using a combination of ab initio and least-square fitting procedures provided by the Cowan suite of codes [49] and extended in our group. Therefore we provide a theoretical interpretation of Ho even-parity levels, which especially results in the prediction of the widely unmeasured Landé g-factors.…”