Precision Measurement of Light Shifts in a Single Trapped Ba⁺ Ion

Using a single trapped barium ion we have developed an rf spectroscopy technique to measure the ratio of the off-resonant vector ac Stark effect (or light shift) in the 6S_1/2 and 5D_5/2 states to 0.1% precision. We find R=Δ_S/Δ_D=-11.494(13) at 514.531 nm where Δ_S,D are the light shifts of the m=±1/2 splittings due to circularly polarized light. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment. By appropriately choosing an off-resonant light shift wavelength one can emphasize the contribution of one or a few dipole matrix elements and precisely determine their values.