Magic wavelength of the $^{138}$Ba$^+$ $6s\;{}^2S_{1/2}-5d\;{}^2D_{5/2}$ clock transition

TL;DR

This paper precisely measures the zero crossing of the dynamic differential scalar polarizability for the $^{138}$Ba$^+$ $6s o 5d$ clock transition, enabling improved estimates of blackbody radiation shifts in ion-based optical clocks.

Contribution

It provides a highly accurate determination of the zero crossing frequency, constraining the polarizability and blackbody shift estimates for the $^{138}$Ba$^+$ clock transition.

Findings

Zero crossing at 459.1614(28) THz identified.

Enhanced constraints on the differential scalar polarizability.

Improved estimate of blackbody radiation shift at room temperature.

Abstract

The zero crossing of the dynamic differential scalar polarizability of the $S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be $459.1614(28)\,$THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\gtrsim 700\,$nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.