Progress on multi-ion optical clock with $^{176}\mathrm{Lu}^+$

The stability of the current generation of ion-based optical clocks is limited due to the restriction to single-ion operation. Multi-ion operation is complicated by inhomogenous magnetic fields, micromotion-related shifts induced by the trapping radio-frequency field, and electric quadrupole shifts arising from the Coulomb fields of neighboring ions. The three clock transitions in $^{176}\mathrm{Lu}^+$ have favorable properties for multi-ion operation including, low sensitivity to magnetic fields, low differential static scalar polarizability, and the quadrupole shifts can be suppressed by appropriate orientation of the applied magnetic field. Here, we report progress on establishing clock operation on a small linear Coulomb crystal of lutetium ions.