Ytterbium in quantum gases and atomic clocks: van der Waals interactions and blackbody shifts

We evaluated the $C_6$ coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2\% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, $C_6=1929(39)$ a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb $6s^{2}~ ^1\!$S$_0 - 6s6p ~^3\!$P$_0^o$ clock transition with 3.5\% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the $10^{-18}$ level.