Anisotropic light-shift and magic-polarization of the intercombination line of Dysprosium atoms in a far-detuned dipole trap

We characterize the anisotropic differential ac-Stark shift for the Dy $626$ nm intercombination transition, induced in a far-detuned $1070$ nm optical dipole trap, and observe the existence of a "magic polarization" for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, $\alpha_E^\text{s} = 188 (12)\,\alpha_\text{0}$ and $\alpha_E^\text{t} = 34 (12)\,\alpha_\text{0}$, respectively, where $\alpha_\text{0}$ is the atomic unit for the electric polarizability. We also provide a theoretical model allowing us to predict the excited state polari…