Precision Measurement of Light Shifts in a Single TrappedBa+Ion

Abstract

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 S = D ÿ11:49413 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 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.Experimental tests of atomic theory often involve the measurement of atomic state lifetimes, oscillator strengths, polarizabilities [1], and other properties which depend directly on atomic dipole matrix elements. Absolute measurements of these quantities can be difficult. Another approach [2] is to make high precision measurements of properties which can be directly calculated using modern atomic theory techniques and depend on ratios of atomic matrix elements. Here we report a 0.1% measurement of the ratio R of the ac Stark effect [or light shift (LS)] in the 6S 1=2 and 5D 3=2 states of a singly ionized barium ion, isoelectronic to the well-studied alkali atom Cs. Comparison of this result with an ab initio calculation of R would yield a new test of atomic theory.Since R is expressible as ratios of matrix elements (shown below), this measurement also establishes a sum rule relating the barium matrix elements known to 1% or better (i.e., h6S 1=2 jjrjj6P 1=2;3=2 i) to matrix elements with about 10 times worse experimental precision [3-6]. One of the latter, h5D 3=2 jjrjj6P 1=2 i, is crucial for a proposed atomic parity violation experiment [7][8][9]. In our scheme, a particular matrix element can be studied by choosing a light shift wavelength close to the corresponding dipole transition so that other contributions remain small. The technique is generalizable to other trapped ion species with metastable states.To second order in perturbation theory an off-resonant light beam of intensity I, frequency !, and polarization causes a frequency shift k;m in atomic level jk; mi ofwhere is the fine-structure constant, k stands for atomic quantum numbers nlj, and W k is the unperturbed energy of level k. The sums extend over continuum states. Though it is difficult to measure the light intensity at the site of a trapped ion, I cancels in a measured ratio of light shifts. The light shift due to circularly polarized off-resonant light acts effectively as a magnetic field pointing along the direction of light propagation [10,11]. In our case, a laboratory magnetic field (B 0 2:5 G) is aligned with the light shift beam (see Fig. 1). Therefore, if the same magnetic sublevels in two atomic states are used, there is only second order dependence of the ratio on polarization errors and misalignment of the li...

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