Blackbody radiation shift assessment for a lutetium ion clock

We measure the dynamic differential scalar polarizabilities at 10.6 $\mu$m for two candidate clock transitions in ${}^{176}{\mathrm{L}\mathrm{u}}^{+}$. The fractional black body radiation (BBR) shifts at 300 K for the $^1S_0 \leftrightarrow {^3D_1}$and$^1S_0 \leftrightarrow {^3D_2}$transitionsareevaluatedtobe$-1.36,(9) \times 10^{-18}$and$2.70 ,(21) \times10^{-17}$, respectively. The former is the lowest of any established optical atomic clock.