Dynamic polarizabilities and related properties of clock states of the ytterbium atom

We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s^{2 1}S₀ and the first excited 6s6p ³P^o₀ states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s^{2 1}S₀–6s6p ³P^o₀ transition. We determine (i) the first four 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 fourth magic wavelengths to be 551 nm, 465 nm and 413 nm. (ii) We re-evaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at T = 300 K being −1.41(17) Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C₆(6s^{2 1}S₀ + 6s^{2 1}S₀) = 1909(160), C₆(6s^{2 1}S₀ + 6s6p ³P₀) = 2709(338) and C₆(6s6p ³P₀ + 6s6p ³P₀) = 3886(360). Finally, we determine the atom-wall interaction coefficients (in a.u.), C₃(6s^{2 1}S₀) = 3.34 and C₃(6s6p ³P₀) = 3.68. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.