Anomalously small blackbody radiation shift in Tl+ frequency standard

TL;DR

This paper calculates the blackbody radiation shift in Tl+ atomic clock transition, revealing an exceptionally small shift due to near cancellation of polarizabilities, which enhances the accuracy of Tl+ as a frequency standard.

Contribution

It provides the first detailed calculation of the BBR shift in Tl+ using advanced methods, showing its potential for highly precise atomic clocks due to minimal BBR effects.

Findings

BBR shift in Tl+ is approximately -0.0157 Hz at 300K

Tl+ has the smallest fractional BBR shift among known frequency standards

The BBR contribution limits fractional frequency uncertainty to 1×10^{-18}

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 $6s^2 ^1S_0$ and $6s6p ^3P_0$ states of Tl$^+$ ion; we find $\alpha_0(^1S_0)=19.6$ a.u. and $\alpha_0(^3P_0)=21.4$ a.u.. The resulting BBR shift of the $6s6p ^3P_0 - 6s^2 ^1S_0$ Tl$^+$ transition at $300 K$ is $\Delta \nu_{\rm BBR}=-0.0157(16)$ Hz. This result demonstrates that near cancelation of the $^1S_0$ and $^3P_0$ state polarizabilities in divalent B+, Al+, In$^+$ ions of group IIIB [Safronova \textit{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 $1\times10^{-18}$. We find that Tl+ has the smallest fractional BBR shift among all present or proposed frequency standards with the exception of Al+.