We report a high-accuracy measurement of the differential static scalar polarizability $\mathrm{\Delta }{\alpha }_0$ of the $5s{}^2{S}_{1/2}-4d{}^2{D}_{5/2}$ transition of the ${}^{88}{\mathrm{Sr}}^{+}$ ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine $\mathrm{\Delta }{\alpha }_0$ without the need to determine the electric field. $\mathrm{\Delta }{\alpha }_0$ is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the ${}^{88}{\mathrm{Sr}}^{+}$ ion clock. The measured value of $\mathrm{\Delta }{\alpha }_0$ is $-4.7938(71)\times 10^{-40}\mathrm{J}{\mathrm{m}}^2/{\mathrm{V}}^2$. Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247 99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from $2\times 10^{-17}$ to $8.3\times 10^{-19}$. The revised total uncertainty of our reference standard is $1.2\times 10^{-17}$, limited by the blackbody field evaluation. An additional benefit of the low uncertainty of $\mathrm{\Delta }{\alpha }_0$ is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

• Received 27 February 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.173002