Anomalously small blackbody radiation shift in the Tl+frequency standard

Abstract

The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature of which the leading contributor is the blackbody radiation (BBR) shift. In the present work, we used configuration interaction $+$ coupled-cluster method to evaluate polarizabilities of the $6{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$ states of the Tl${}^{+}$ ion; we find ${\ensuremath{\alpha}}_{0}{(}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0})=19.6$ a.u. and ${\ensuremath{\alpha}}_{0}{(}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0})=21.4$ a.u. The resulting BBR shift of the $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}\ensuremath{-}6{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ Tl${}^{+}$ transition at 300 K is $\ensuremath{\Delta}{\ensuremath{\nu}}_{\mathrm{BBR}}=\ensuremath{-}0.0157(16)$ Hz. This result demonstrates that near cancellation of the ${}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$ and ${}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$ state polarizabilities in divalent B${}^{+}$, Al${}^{+}$, and In${}^{+}$ ions of group IIIB [M. S. Safronova et al., Phys. Rev. Lett. 107, 143006 (2011)] continues for much heavier Tl${}^{+}$, leading to anomalously small BBR shift for this system. This calculation demonstrates that the BBR contribution to the fractional frequency uncertainty of the Tl${}^{+}$ frequency standard at 300 K is $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. We find that Tl${}^{+}$ has the smallest fractional BBR shift among all present or proposed frequency standards with the exception of Al${}^{+}$.