Nuclear magnetic octupole moment and the hyperfine structure of the $5D_{3/2,5/2}$ states of the ${\text{Ba}}^{+}$ ion

The hyperfine structure of the long-lived $5D_{3/2}$ and $5D_{5/2}$ levels of ${\text{Ba}}^{+}$ ion is analyzed. A procedure for extracting relatively unexplored nuclear magnetic moments $\Omega$ is presented. The relevant electronic matrix elements are computed in the framework of the ab initio relativistic many-body perturbation theory. Both the first- and the second-order (in the hyperfine interaction) corrections to the energy levels are analyzed. It is shown that a simultaneous measurement of the hyperfine structure of the entire $5D_J$ fine-structure manifold allows one to extract $\Omega$ without contamination from the second-order corrections. Measurements to the required accuracy should be possible with a single trapped barium ion using sensitive techniques already demonstrated in ${\text{Ba}}^{+}$ experiments.

Figure 1

The lowest $S$, $P$, and $D$ states of ${\text{Ba}}^{+}$, showing the cooling 493 nm and cleanup 650 nm transitions plus the 2051 nm and 1762 nm $E2$ transitions to the metastable $D$ states.

Figure 2

Procedure for measuring the hyperfine intervals in the $5D_{5/2}$ state. (a) First, a 1762 nm resonant laser pulse transfers the ion into the $F=2$ hyperfine sublevel of the $5D_{5/2}$ state. (b) The rf is then applied to drive a hyperfine transition in the $5D_{5/2}$ state. (c) The second pulse of the 1762 nm laser depopulates the $5D_{5/2}$ $F=2$ level. (d) To determine if the hyperfine transition in the $5D_{5/2}$ state occurred, the cooling and the cleanup lasers are turned on and any ion fluorescence is detected. Absence of fluorescence indicates that the rf is on resonance and caused the transition to take place.

Figure 3

$D_{5/2}$ $F=3$ and $F=4$ hyperfine Zeeman levels. Energies are measured relative to the $F=4$ energy at zero magnetic field. Very small mixing of the $F=3$ state with the $F=2$ state has been neglected.