ECAMP 15

Atomic clocks realize unperturbed transition frequencies of atoms or ions. For clocks operated at room temperature, the Stark shift from thermal radiation of the environment causes the largest frequency shift and needs to be corrected for with high accuracy. In ion-based systems two methods have been employed to assess the sensitivity of the transition frequency to room-temperature blackbody radiation. For most ion species, the differential polarizability $\Delta \alpha$ is obtained via frequency shifts from intense laser radiation at infrared or near-infrared wavelengths. The intensity of the perturbing laser field is derived from estimations of the intensity profile at the position of the trapped ion and the optical power of the beam. Here, uncertainties of a few percent result from the optical power measurements and the limited knowledge of the intensity distribution [1, 2].

More accurate determinations are possible, if the Stark shift increases the reference transition frequency, which corresponds to a negative differential polarizability. In this case, the sensitivity can be calculated from the “magic” frequency of the field trapping the ion. Here, the Stark and relativistic Doppler shift from excess micromotion, the driven motion of the ion in the trapping field, cancel. For $\text{Sr}^+$ and $\text{Ca}^+$ clock transitions $\Delta\alpha$ has been measured with uncertainties of 0.15% and 0.06% [3, 4].

We present results from a complementary measurement of $\Delta\alpha$ for the $\phantom{}^{88}\text{Sr}^+$ clock transition using perturbing laser radiation. Interestingly, we find a difference of 13% corresponding to $4 \sigma$ significance between the two approaches. By operating a dual species clock with $\phantom{}^{171}\text{Yb}^+$ and $\phantom{}^{88}\text{Sr}^+$, we can subject both ion species to the same laser intensity and measure their polarizability ratio. We find that the ratio is consistent with independent determinations of the polarizability for each ion species using perturbing laser radiation. But they show the same discrepancy to the polarizability obtained via the “magic” trap drive frequency, supporting that the disagreement is due to the methods themselves. We aim to determine which value of the $\text{Sr}^+$ polarizability is correct with a direct measurement of the $\phantom{}^{88}\text{Sr}^+$ frequency at different environmental temperatures.

[1] N. Huntemann et al., “Single-Ion Atomic Clock with $3 \times 10^{−18}$ Systematic Uncertainty”, Phys. Rev. Lett. 116, 063001 (2016)
[2] K. J. Arnold et al., “Blackbody radiation shift assessment for a lutetium ion clock”, Nature Communications 9, 1650 (2018)
[3] P. Dubé et al., “High-Accuracy Measurement of the Differential Scalar Polarizability of a $\phantom{}^{88}\text{Sr}^+$ Clock Using the Time-Dilation Effect”, Phys. Rev. Lett. 112, 173002 (2014)
[4] Y. Huang et al., “$\phantom{}^{40}\text{Ca}^+$ ion optical clock with micromotion-induced shifts below $1 \times 10^{−18}$”, Phys. Rev. A 99, 011401(R) (2019)