Hyperfine-mediated effects in a Lu$^+$ optical clock

Abstract

We consider hyperfine-mediated effects for clock transitions in 176 Lu + . Mixing of fine structure levels due to the hyperfine interaction bring about modifications to Landé g-factors and the quadrupole moment for a given state. Explicit expressions are derived for both g-factor and quadrupole corrections, for which leading order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the g-factors for the 1 S0 and 3 D1 hyperfine levels are carried out, which provide an experimental determination of the leading order correction terms.