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

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 $⟨P_{3/2}\Vert r\Vert S_{1/2}⟩/⟨P_{1/2}\Vert r\Vert S_{1/2}⟩=1.41181(13)$, 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, $⟨P_{1/2}\Vert r\Vert S_{1/2}⟩$, 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.

8 pages, 5 figures

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