Measurement of the Differential Static Scalar Polarizability of the $^\mathbf{88}$Sr$^{+}$ Clock Transition

TL;DR

This paper presents a highly precise measurement of the differential static scalar polarizability of the $^{88}$Sr$^{+}$ ion's clock transition, significantly reducing uncertainty and improving atomic clock accuracy.

Contribution

The study introduces a novel measurement technique that minimizes systematic uncertainties in polarizability determination, achieving a 3.5-fold reduction in uncertainty compared to previous results.

Findings

Measured $ extstyle riangleeta_0$ with high precision

Reduced polarizability uncertainty by a factor of 3.5

Achieved a total uncertainty below $1 imes 10^{-18}$

Abstract

We report on a precision measurement of the differential static scalar polarizability $\Delta\alpha_0$ of the ${}^{2}\!S_{1/2} \rightarrow {}^{2}\!D_{5/2}$ optical clock transition in the $^{88}$Sr$^{+}$ ion. The polarizability was determined from the 'magic' ion-trap drive frequency where the micromotion-induced second-order Doppler and quadratic Stark shifts cancel, using a single clock in an interleaved scheme by switching between minimized and large micromotion. By measuring at different Mathieu $q_z$ parameters, $\Delta\alpha_0$ can be obtained without prior knowledge of the angle between the rf electric field and the trap axis, which would otherwise dominate the systematic uncertainty. For validation, measurements were carried out at different micromotion levels and by displacing the ion in opposite directions. The results show excellent consistency and our value, $\Delta\alpha_0 = -4.8314(20)\times 10^{-40}\;\mathrm{J\, m^2/V^2} = -29.303(12)\;\mathrm{au}$, reduces the uncertainty by a factor of 3.5 compared to a previous measurement, while showing a discrepancy of $5 \sigma$. Our measurement reduces the polarizability-related uncertainty of the $^{88}$Sr$^{+}$ clock to $2.2\times 10^{-19}$ for a blackbody radiation temperature of 295 K -- a significant step towards total uncertainties ${<}1\times10^{-18}$. Using existing polarizability transfer schemes, the result can reduce the uncertainty also for other ion species.