Towards a Measurement of the Nuclear Magnetic Octupole Moment of $^{137}$Ba

Measurements of hyperfine structure in a $^{133}$Cs atom resolved a nuclear magnetic octupole moment, $\Omega$, much larger than expected.\footnote{V. Gerginov, A. Derevianko, and C. E. Tanner, Phys. Rev. Lett. 91, 072501} To explore this anomaly further, we are undertaking an experiment to measure the hyperfine structure of the 5D levels of $^{137}$Ba. We will selectively populate the m=0 states in the 5D$_{3/2}$ manifold by driving the 6S$_{1/2}$ to 5D$_{3/2}$ electric quadrupole transition using a commercially available Tm,Ho:YLF laser. Using the Pound-Drever-Hall frequency stabilization method we locked this laser to a high finesse cavity made of ULE glass and demonstrated a laser linewidth of less than 750 Hz. Once the barium ion is initialized to an m=0 state of a chosen 5D$_{3/2}$ hyperfine sublevel, we will perform RF spectroscopy to measure the hyperfine splittings with mHz precision. A measurement the 5D$_{3/2}$ hyperfine intervals combined with a similar measurement of the 5D$_{5/2}$ hyperfine intervals (using a 1762 nm fiber laser) will allow theorists to extract a value for $\Omega$.