Optical trapping of ultracold dysprosium atoms: transition probabilities, dynamic dipole polarizabilities and van der Waals $C_6$ coefficients

TL;DR

This paper calculates the dynamic dipole polarizabilities, transition probabilities, and van der Waals coefficients for ultracold dysprosium atoms, providing essential data for optimizing optical trapping and understanding atom interactions.

Contribution

It presents comprehensive calculations of polarizabilities, transition probabilities, and $C_6$ coefficients for dysprosium using a combination of ab initio and fitting methods, extending existing data.

Findings

Scalar polarizability dominates at far-from-resonance frequencies.

Vector and tensor contributions are significant for imaginary polarizability.

Calculated $C_6$ coefficients inform on van der Waals interactions.

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 \textit{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.