Anomalously small blackbody radiation shift in Tl+ frequency standard

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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 6s² ¹S₀ and 6s6p ³P₀ states of Tl+ ion; we find α₀(¹S₀)=19.6 a.u. and α₀(³P₀)=21.4 a.u.. The resulting BBR shift of the 6s6p ³P₀ - 6s² ¹S₀ Tl+ transition at 300 K is Δν BBR=-0.0157(16) Hz. This result demonstrates that near cancelation of the ¹S₀ and ³P₀ state polarizabilities in divalent B+, Al+, In+ ions of group IIIB [Safronova et al., PRL 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 300K is 1×10⁻¹⁸. We find that Tl+ has the smallest fractional BBR shift among all present or proposed frequency standards with the exception of Al+.