Static and dynamic polarizabilities of Yb-ion]{Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the $6{\mathrm{S}}_{1/2}\to 5{\mathrm{D}}_{3/2}$ clock transition in Yb${}^{+}$

Abstract

We present precise values of the dipole polarizabilities ($\hat{I}\pm$) of the ground $[4{\mathrm{f}}^{14}6s]{}^2{\mathrm{S}}_{1/2}$ and metastable $[4{\mathrm{f}}^{14}5d]{}^2{\mathrm{D}}_{3/2}$ states of Yb${}^{+}$, that are %vital {\bf important} in reducing systematics in the clock frequency of the $[4{\mathrm{f}}^{14}6s]{}^2{\mathrm{S}}_{1/2}\to [4{\mathrm{f}}^{14}5d]{}^2{\mathrm{D}}_{3/2}$ transition. The static values of $\hat{I}\pm$ for the ground and $[4{\mathrm{f}}^{14}5d]{}^2{\mathrm{D}}_{3/2}$ states are estimated to be $9.8(1)\times 10^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$ and $17.6(5)\times 10^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$, respectively, while the tensor contribution to the $[4{\mathrm{f}}^{14}5d]{}^2{\mathrm{D}}_{3/2}$ state as $-12.3(3)\times 10^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$ compared to the experimental value $-13.6(2.2)\times 10^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$. This corresponds to the differential scalar polarizability value of the above transition as $-7.8$(5)$\times 10^{-40}\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$ in contrast to the available experimental value $-6.9$(1.4)$\times 10^{-40}$\,\, $\mathrm{J}{\mathrm{m}}^2{\mathrm{V}}^{-2}$. This results in the black-body radiation (BBR) shift of the clock transition as $-0.44(3)$ Hz at the room temperature, which is large as compared to the previously estimated values. Using the dynamic $\hat{I}\pm$ values, we report the tune-out and magic wavelengths that could be of interest to subdue %major systematics due to the Stark shifts and for constructing lattice optical clock using Yb${}^{+}$.

18 pages, 3 figures