Suppressing Inhomogeneous Broadening in a Lutetium Multi-ion Optical Clock

We demonstrate precision measurement and control of inhomogeneous broadening in a multi-ion clock consisting of three ¹⁷⁶Lu⁺ ions. Microwave spectroscopy between hyperfine states in the ³D₁ level is used to characterize 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 ~10^-17 level relative to the ¹S₀↔³D₁ optical transition frequency. Correlation spectroscopy on the optical transition demonstrates the feasibility of a 10-s Ramsey interrogation in the three ion configuration with a corresponding projection noise limited stability of σ(τ)=8.2×10^-17/√τ.