Precision measurement of branching fractions of ${}^{138}\mathrm{Ba}{}^{+}$: Testing many-body theories below the 1% level

The branching fractions from the excited state $6P_{1/2}$ of singly charged barium ion has been measured with a precision $0.03\%$ in an ion trap experiment. This measurement along with the known value of the upper state lifetime allowed the determination of the dipole matrix elements for the transitions $P\text{−}S$ and $P\text{−}D$ to below the $1\%$ level. Therefore, it is now possible to compare the many-body calculations of these matrix elements at a level which is of significance to any parity-nonconservation experiment on barium ion. Moreover, these dipole matrix elements are the most significant contributors to the parity-violating matrix element between the $S\text{−}D$ transition, contributing up to $90\%$ to the total. Our results on the dipole matrix elements are $3.305\pm 0.014$ a.u. and $3.042\pm 0.016$ a.u. for the $S\text{−}P$ and $P\text{−}D$ transitions, respectively.

Figure 1

Schematic diagram of our experiment: During the experiment, AO1 and AO3 are switched using a DDS controlled by NIDAQ. Relevant atomic levels of $\mathrm{Ba}{}^{+}$ ions are also shown. The branching fractions reported here are $r$ and $1-r$ for the two decay channels while the upper state lifetime is the best literature value available [22].

Figure 2

Experimental sequence and green photon count measurement. The top panel shows the experimental time sequence of the green and red pulses, while the corresponding photon counts are shown in the middle panel. The sequence consists of (a) green photon measurement (green laser on), (b) green background counts (green laser on), (c) cooling (both lasers on), (d) optical pumping to $D$ state (green laser on), (e) red repumping while green photon counting (red laser on), (f) dark count measurement (both lasers off), and (c) another cooling pulse. The lower panel shows zoomed parts of both the decay curves due to transfer and back transfer of population.

Figure 3

A comparison of different measurements (open square) and theory (filled square) values of the dipole transition probabilities for $S\text{−}P$ (left) and $D\text{−}P$ (right) transitions. The hatched area provides the value and $1\sigma$ confidence band of this measurement. The values by [24, 26] are compilation results of previous experiments.