Measurement of the reduced dipole matrix element in Ba${}^{+}$

Abstract

We present a high-precision measurement of the reduced electric-dipole matrix element $⟨P_{1/2}\Vert r\Vert S_{1/2}⟩$ in ${}^{138}{\mathrm{Ba}}^{+}$. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be $3.3227(12)$, corresponding to a $P_{1/2}$ excited-state radiative lifetime of $7.8663(56)$~ns. Combining our experimental results with a prior model for the differential scalar polarizability $\Delta {\alpha }_0(\omega )$, we extract the static value $\Delta {\alpha }_0(0)=-73.09(12)$a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature ${\mathrm{Ba}}^{+}$ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.

8 pages, 6 figures