Measurement of light shifts at two off-resonant wavelengths in a single trapped Ba⁺ ion and the determination of atomic dipole matrix elements

We have measured the ratio R of the vector ac Stark effect (or light shift) in the 6S_1∕2 and 5D_3∕2 states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found R=Δ_S∕Δ_D=−11.494(13) at 514.531 nm where Δ_S,D are the vector light shifts of the 6S_1∕2 and 5D_3∕2 m=±1∕2 splittings due to circularly polarized light, and now we report the value at 1111.68 nm, R=+0.4176(8). These observations together yield a value of the ⟨5D‖er‖4F⟩ matrix element. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.