# Polarizability assessments of ion-based optical clocks

## TL;DR

This paper demonstrates a method to accurately determine the dynamic differential scalar polarizability of ion-based optical clock transitions, enabling precise in situ laser intensity measurements and improving clock accuracy.

## Contribution

It introduces a measurement approach that achieves sub-0.5% accuracy in polarizability assessments without requiring precise laser intensity calibration.

## Key findings

- Achieves below 0.5% inaccuracy in polarizability measurement across wavelengths >700 nm.
- Enables in situ laser intensity calibration via ac-stark shift measurements.
- Applicable to multiple ion species including Ba+, Sr+, Ca+, and Al+/Ca+ clocks.

## Abstract

It is shown that the dynamic differential scalar polarisability of the $S_{1/2}-D_{5/2}$ transition in $^{138}$Ba$^+$ can be determined to an inaccuracy below $0.5\%$ across a wide wavelength range ($\lambda>700\,\mathrm{nm}$). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-stark shift of the clock transition would then provide an \emph{in situ} measurement of the laser's intensity to the same $0.5\%$ level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarisability measurements for clock transitions in other ions, through comparison with $^{138}$Ba$^+$. The approach would be equally applicable to Sr$^+$ and Ca$^+$, with the latter being immediately applicable to Al$^+$/Ca$^+$ quantum logic clocks.