Precision Calculation of Blackbody Radiation Shifts for Optical Frequency Metrology

We show that three group IIIB divalent ions, ${\mathrm{B}}^{+}$, ${\mathrm{Al}}^{+}$, and ${\mathrm{In}}^{+}$, have anomalously small blackbody radiation (BBR) shifts of the $n{s}^2$ ${}^{1}S_0-nsnp$ ${}^{3}P_0^o$ clock transitions. The fractional BBR shifts for these ions are at least 10 times smaller than those of any other present or proposed optical frequency standards at the same temperature, and are less than 0.3% of the Sr clock shift. We have developed a hybrid configuration-interaction + coupled-cluster method that provides accurate treatment of correlation corrections in such ions and yields a rigorous upper bound on the uncertainty of the final results. We reduce the BBR contribution to the fractional frequency uncertainty of the ${\mathrm{Al}}^{+}$ clock to $4\times {10}^{-19}$ at $T=300\mathrm{K}$. We also reduce the uncertainties due to this effect at room temperature to ${10}^{-18}$ level for ${\mathrm{B}}^{+}$ and ${\mathrm{In}}^{+}$ to facilitate further development of these systems for metrology and quantum sensing.