Zero crossings of the differential scalar polarizability of Ba$^+$ clock transition

TL;DR

This paper measures the zero crossing of the differential scalar polarizability of Ba$^+$ clock transition near 481nm, providing precise atomic data and an accurate model for frequency-dependent polarizability relevant to ion clock accuracy.

Contribution

It reports a precise measurement of the zero crossing and derives a simplified model for polarizability, aiding atomic structure tests and clock shift assessments.

Findings

Zero crossing near 481nm measured at 623.60313 THz.

Derived ratio of reduced matrix elements: 1.41181.

Model enables accurate BBR shift evaluation for ion clocks.

Abstract

The differential scalar polarizability $\Delta\alpha_0(\omega)$ of the Ba$^+$ S$_{1/2}$-to-D$_{5/2}$ clock transition has a zero crossing near 481nm, which is measured to be 623.603\,13(17)\,THz. From this measurement, we infer a ratio of reduced matrix elements $\langle P_{3/2}\|r\|S_{1/2}\rangle/\langle P_{1/2}\|r\|S_{1/2}\rangle=1.411\,81(13)$, which provides a stringent test of atomic structure calculations and experimental determination of matrix elements. Additionally, it enables the construction of an accurate approximation to $\Delta\alpha_0(\omega)$, valid for frequencies up to 450\,THz, with only one reduced matrix element, $\langle P_{1/2}\|r\|S_{1/2}\rangle$, appearing in the model's parameterization. We discuss the achievable accuracy of the model, the application to the assessment of blackbody radiation (BBR) shifts in ion-based clocks, and the applicability of the approach to other alkaline-earth ions.