ar X iv : p hy si cs / 0 50 21 13 v 1 2 2 Fe b 20 05 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 6S1/2 and 5D3/2 states to 0.1% precision. We find R ≡ ∆S/∆D = −11.494(13) at 514.531 nm where ∆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. 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.