Transition frequencies between low-lying energy levels in a single trapped $^{138}$Ba$^{+}$ ion have been measured with laser spectroscopy referenced to an optical frequency comb. By extracting the frequencies of one-photon and two-photon components of the line shape using an eight-level optical Bloch model, we achieved 0.1 MHz accuracy for the 5d $^{2}$D$_{3/2}$ - 6p $^{2}$P$_{1/2}$ and 6s $^{2}$S$_{1/2}$ - 5d $^{2}$D$_{3/2}$ transition frequencies, and 0.2 MHz for the 6s $^{2}$S$_{1/2}$ - 6p $^{2}$P$_{1/2}$ transition frequency.
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_{3/2} states to 0.1% precision. We find R = Delta_S / Delta_D = -11.494(13) at 514.531 nm where Delta_{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.
The zero crossing of the dynamic differential scalar polarizability of the $S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be $459.1614(28),$THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($gtrsim 700,$nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.
We define and measure 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 = -11.494(13) at 514.531nm and now report the value at 1111.68nm, R = +0.4176(8). These observations together yield a value of the <5D||er||4F> matrix element, previously unknown in the literature. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.
Measurement of the $^{138}$Ba$^+$ ${}^2S_{1/2} - {}^2D_{5/2}$ clock transition frequency and $D_{5/2}$ Lande $g_J$ factor are reported. The clock transition frequency $ u_{mathrm{Ba}^+}=170,126,432,449,333.31pm(0.39)_mathrm{stat}pm(0.29)_mathrm{sys},$Hz, is obtained with accuracy limited by the frequency calibration of the maser used as a reference oscillator. The Land{e} $g_J$-factor for the ${}^2D_{5/2}$ level is determined to be $g_{D}=1.200,367,39(24)$, which is a 30-fold improvement on previous measurements. The $g$-factor measurements are corrected for an ac-magnetic field from trap-drive-induced currents in the electrodes, and data taken over a range of magnetic fields underscores the importance of accounting for this systematic.
Measurement of the branching ratios for $6P_{1/2}$ decays to $6S_{1/2}$ and $5D_{3/2}$ in $^{138}$Ba$^+$ are reported with the decay probability from $6P_{1/2}$ to $5D_{3/2}$ measured to be $p=0.268177pm(37)_mathrm{stat}-(20)_mathrm{sys}$. This result differs from a recent report by $12sigma$. A detailed account of systematics is given and the likely source of the discrepancy is identified. The new value of the branching ratio is combined with a previous experimental results to give a new estimate of $tau=7.855(10),mathrm{ns}$ for the $6P_{1/2}$ lifetime. In addition, ratios of matrix elements calculated from theory are combined with experimental results to provide improved theoretical estimates of the $6P_{3/2}$ lifetime and the associated matrix elements.