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The efficiency of optical trapping of ultracold atoms depend on the atomicdynamic dipole polarizability governing the atom-field interaction. In thisarticle, we have calculated the real and imaginary parts of the dynamic dipolepolarizability of dysprosium in the ground and first excited level. Due to thehigh electronic angular momentum of those two states, the polarizabilitiespossess scalar, vector and tensor contributions that we have computed, on awide range of trapping wavelengths, using the sum-over-state formula. Using thesame formalism, we have also calculated the $C_6$ coefficients characterizingthe van der Waals interaction between two dysprosium atoms in the two lowestlevels. We have computed the energies of excited states and the transitionprobabilities appearing in the sums, using a combination of \textit{ab initio}and least-square-fitting techniques provided by the Cowan codes and extended inour group. Regarding the real part of the polarizability, for field frequenciesfar from atomic resonances, the vector and tensor contributions aretwo-order-of-magnitude smaller than the scalar contribution, whereas for theimaginary part, the vector and tensor contributions represent a noticeablefraction of the scalar contribution. This offers the possibility to control thedecoherence and trap losses due to spontaneous emission.

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