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

TL;DR

This paper investigates hyperfine-mediated effects in the Lu$^+$ optical clock, deriving explicit formulas for corrections to $g$-factors and quadrupole moments, supported by high-precision measurements.

Contribution

It provides new explicit expressions for hyperfine-induced corrections and experimentally measures $g$-factors in Lu$^+$, enhancing understanding of hyperfine effects in optical clocks.

Findings

Derived explicit formulas for $g$-factor and quadrupole corrections.

Measured $g$-factors for hyperfine levels with high accuracy.

Quantified hyperfine-mediated modifications in Lu$^+$ clock states.

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 Land\'e $g$-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 $^1S_0$ and $^3D_1$ hyperfine levels are carried out, which provide an experimental determination of the leading order correction terms.