Dynamic polarizabilities and related properties of clock states of ytterbium atom

We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground $6s^2 ^1S_0$ and the first excited $6s6p ^3P^o_0$ states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the $6s^2 ^1S_0 - 6s6p ^3P^o_0$ transition. We determine (i) the first four {\em magic} wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the forth magic wavelengths to be 551 nm, 465 nm, and 413 nm. (ii) We reevaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at $T=300 \mathrm{K}$ being $-1.41(17)$ Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) $C_6(6s^2 ^1S_0 +6s^2 ^1S_0) = 1909(160)$, $C_6(6s^2 ^1S_0 + 6s6p ^3P_0) =2709(338) $, and $C_6(6s6p ^3P_0 + 6s6p ^3P_0) =3886(360) $. Finally, we determine the atom-wall interaction coefficients (in a.u.), $C_3 (6s^2 ^1S_0) =3.34$ and $C_3 (6s6p ^3P_0) =3.68$. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.