Measurement of the branching ratio in the $6P_{3∕2}$ decay of $\mathrm{Ba}\mathrm{II}$ with a single trapped ion

We present a measurement of the branching ratios from the $6P_{3∕2}$ state of $\mathrm{Ba}\mathrm{II}$ into all dipole-allowed decay channels ($6S_{1∕2}$, $5D_{3∕2}$, and $5D_{5∕2}$). Measurements were performed on single ${}^{138}{\mathrm{Ba}}^{+}$ ions in a linear Paul trap with a frequency-doubled mode-locked Ti:sapphire laser resonant with the $6S_{1∕2}\to 6P_{3∕2}$ transition at $455\mathrm{nm}$ by detection of electron shelving into the dark $5D_{5∕2}$ state. By driving a $\pi$ Rabi rotation with a single femtosecond pulse, an absolute measurement of the branching ratio to $5D_{5∕2}$ state was performed. Combined with a measurement of the relative decay rates into $5D_{3∕2}$ and $5D_{5∕2}$ states performed with long trains of highly attenuated $455\mathrm{nm}$ pulses, it allowed the extraction of the absolute ratios of the other two decays. Relative strengths normalized to unity are found to be $0.756\pm 0.046$, $0.0290\pm 0.0015$, and $0.215\pm 0.0064$ for $6S_{1∕2}$, $5D_{3∕2}$, and $5D_{5∕2}$, respectively. This approximately constitutes a threefold improvement over the best previous measurements and is a sufficient level of precision to compare to calculated values for dipole matrix elements.

Figure 1

Schematic overview of the apparatus used in this experiment. After stabilization to their respective gas cells, cooling $\left(493\mathrm{nm}\right)$ and repump lasers $\left(650\mathrm{nm}\right)$ are coupled on a dichroic mirror and fiber coupled for mode-cleaning and to ensure collinearity. Detection of ion fluorescence, after collection optics and filtering through a $493\mathrm{nm}$ narrowband interference filter, can be switched between a cooled electron-multiplied CCD (EMCCD) Andor iXon camera with single photon sensitivity or a Hamamatsu photomultiplier tube (PMT). The xenon flash lamp has high spectral content in the uv and thereby photoionizes a thermal beam of atomic barium. The Ti:sapphire, independently synchronized to the measurement apparatus through the $1.125\mathrm{GHz}$ gate and HP 8031B pulse generator, provides $400\mathrm{fs}$ pulses at $910\mathrm{nm}$ central wavelength, which are doubled to $455\mathrm{nm}$ after a single pass through the BBO crystal. The $614\mathrm{nm}$ high-power LED deshelves the ion from the $5D_{5∕2}$ state.

Figure 2

Relevant energy levels and lifetimes in the ${}^{138}{\mathrm{Ba}}^{+}$ ion. $D$ state lifetimes are experimental values [23]. The decays under consideration are from $6P_{3∕2}$ to $6S_{1∕2}$ at $455.403\mathrm{nm}$, $5D_{3∕2}$ at $585.530\mathrm{nm}$ (not shown in diagram), and $5D_{5∕2}$ at $614.171\mathrm{nm}$.

Figure 3

Representative data obtained to establish a value for the relative strengths of the decays to the two $D$ states in ${}^{138}{\mathrm{Ba}}^{+}$. The ion was exposed to highly attenuated $455\mathrm{nm}$ light, weakly driving it to the $6P_{3∕2}$ state. At long exposure times, the probability that the ion is dark will determine the relative proportion of the trials where the decay from $6P_{3∕2}$ was to $5D_{5∕2}$. The solid line is a fit to the data using a three-parameter model, $P_{\mathrm{dark}}=\Delta +B(1+e^{-\lambda t})$, where the fit parameter $B$ determines the ratio of the relative strengths of the $D$ state decays.

Figure 4

Data obtained from single pulse excitation of the $6S_{1∕2}\to 6P_{3∕2}$ transition. Shelving probability represents the percentage of the runs where upon spontaneous decay, the ion was no longer fluorescing, i.e., it was in the $5D_{5∕2}$ state. The solid line is a two-parameter fit to the data using $P_{\mathrm{dark}}=B^{\prime }{\sin }^2(\alpha \sqrt{E}∕2)$, from which the value for the branching probability $B^{\prime }$ from $6P_{3∕2}$ to $5D_{5∕2}$ was extracted to be $0.215\pm 0.0047$.

Figure 5

Comparison of presently measured transition rates for the three transitions from $6P_{3∕2}$ to the final state noted at the left vertical axis to previously measured and calculated values. Error bars are one sigma confidence intervals on experimental data. Vertical ordering in lower two panels is the same as topmost panel.