Observation of the nuclear magnetic octupole moment of ${}^{173}$Yb from precise measurements of hyperfine structure in the ${{}^{3}P}_2$ state

We measure hyperfine structure in the metastable ${{}^{3}P}_2$ state of ${}^{173}$Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the ${{}^{3}P}_1$ and ${{}^{3}S}_1$ states. We measure frequencies of hyperfine transitions of the ${^3P}_2 \rightarrow {^3S}_1$ line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby ${{}^{3}P}_1$ and ${{}^{1}P}_1$ states are below 30 kHz. We obtain the hyperfine coefficients as: $A=-742.11(2)$ MHz, $B=1339.2(2)$ MHz, which represent two orders-of-magnitude improvement in precision, and $C=0.54(2)$ MHz. From atomic structure calculations, we obtain the nuclear moments: quadrupole $Q=2.46(12)$ b and octupole $\mathrm{\Omega }=-34.4(21)$ b,$\times {\mu }_N$.