# Spectroscopy of the $^1S_0$-to-$^1D_2$ clock transition in $^{176}$Lu$^+$

## TL;DR

This paper reports high-precision spectroscopy of the $^1S_0$-to-$^1D_2$ clock transition in $^{176}$Lu, achieving Hertz-level accuracy and providing detailed hyperfine structure data, including nuclear moments.

## Contribution

It presents the first high-precision measurement of the $^{176}$Lu$^+$ clock transition and detailed hyperfine structure analysis including nuclear moments.

## Key findings

- Hertz-level precision in frequency measurement
- Accurate hyperfine structure constants for $^{176}$Lu$^+$
- Determination of nuclear magnetic octupole and electric hexadecapole moments

## Abstract

High precision spectroscopy of the $^1S_0$-to-${^1}D_2$ clock transition of $^{176}$Lu is reported. Measurements are performed with Hertz level precision with the accuracy of the hyperfine-averaged frequency limited by the calibration of an active hydrogen maser to the SI definition of the second via a GPS link. The measurements also provide accurate determination of the $^1D_2$ hyperfine structure. Hyperfine structure constants associated with the magnetic octupole and electric hexadecapole moments of the nucleus are considered, which includes a derivation of correction terms from third-order perturbation theory.