Magic wavelength of the ${}^{138}$Ba${}^{+}$ $6s{}^2{S}_{1/2}-5d{}^2{D}_{5/2}$ clock transition

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.

4 pages, 2 figures. Updated based on new branching ratio measurements