Spectroscopy on a single trapped ¹³⁷Ba⁺ ion for nuclear magnetic octupole moment determination

We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, ¹³⁷Ba⁺. Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, Ω, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in ¹³⁷Ba⁺ and the most accurately determined octupole moment to date.