Hyperfine averaging by dynamic decoupling in a multi-ion lutetium clock

We propose and experimentally demonstrate a scheme which effects hyperfine averaging during a Ramsey interrogation of a clock transition. The method eliminates the need to average over multiple optical transitions, reduces the sensitivity of the clock to its environment, and reduces inhomogeneous broadening in a multi-ion clock. The method is compatible with auto-balanced Ramsey spectroscopy, which facilitates elimination of residual shifts due to imperfect implementation and ac Stark shifts from the optical probe. We demonstrate the scheme using correlation spectroscopy of the ${}^1{S}_0$-to-${}^3{D}_1$ clock transition in a three-ion Lu+ clock. From the demonstration we are able to provide a measurement of the ${}^3{D}_1$ quadrupole moment, $\mathrm{\Theta }{(}^3{D}_1)=0.634(9)e{a}_0^2$.