Measurement of the Differential Static Scalar Polarizability of the ⁸⁸Sr⁺ Clock Transition

We report on a precision measurement of the differential static scalar polarizability Δα₀ of the ²S_1/2 → ²D_5/2 optical clock transition in the ⁸⁸Sr⁺ ion. The polarizability was determined from the “magic”ion-trap drive frequency where the micromotion-induced second-order Doppler and quadratic Stark shiftscancel, using a single clock in an interleaved scheme by switching between minimized and largemicromotion. By measuring at different Mathieu q_z parameters, Δα₀ can be obtained without priorknowledge of the angle between the rf electric field and the trap axis, which would otherwise dominate thesystematic uncertainty. For validation, measurements were carried out at different micromotion levels andby displacing the ion in opposite directions. The results show excellent consistency and our value, Δα₀ = −4.8314(20) × 10⁻⁴⁰ Jm²/V² = −29.303(12) au, reduces the uncertainty by a factor of 3.5compared to a previous measurement, while showing a discrepancy of 3.5. Our measurement reducesthe polarizability-related uncertainty of the ⁸⁸Sr⁺ clock to 2.2 × 10⁻¹⁹ for a blackbody radiationtemperature of 295 K—a significant step towards total uncertainties <1 × 10⁻¹⁸. Using existing polarizability transfer schemes, the result can reduce the uncertainty also for other ion species.