# Suppressing inhomogeneous broadening in a lutetium multi-ion optical clock

## TL;DR

This paper demonstrates precise control of inhomogeneous broadening in a multi-ion lutetium optical clock, achieving suppression of systematic shifts to the 10^{-17} level and showing potential for high stability in frequency measurements.

## Contribution

The study introduces a method to suppress inhomogeneous broadening effects in a multi-ion lutetium clock, enabling improved systematic control and stability for optical clock applications.

## Key findings

- Suppression of differential systematic shifts to ~10^{-17} level.
- Feasibility of 10s Ramsey interrogation with high stability.
- Projection noise limited stability of 8.2×10^{-17}/√τ.

## Abstract

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three $^{176}$Lu$^+$ ions. Microwave spectroscopy between hyperfine states in the $^3D_1$ level is used to characterise differential systematic shifts between ions, most notably those associated with the electric quadrupole moment. By appropriate alignment of the magnetic field, we demonstrate suppression of these effects to the $\sim 10^{-17}$ level relative to the $^1S_0\leftrightarrow{}^3D_1$ optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of $\sigma(\tau)=8.2\times 10^{-17}/\sqrt{\tau}$