Operating a Multi-Ion Clock with Dynamical Decoupling

We study and characterize a quasicontinuous dynamical decoupling scheme that effectively suppresses dominant frequency shifts in a multi-ion optical clock. Addressing the challenge of inhomogeneous frequency shifts in such systems, our scheme mitigates primary contributors, namely, the electric quadrupole and the linear Zeeman shifts. Based on ^{88}Sr^{+} ions, we implement the scheme in linear chains of up to 7 ions and demonstrate a significant suppression of the shift by more than 3 orders of magnitude, leading to relative frequency inhomogeneity below 7×10^{-17}. Additionally, we evaluate the associated systematic shift arising from the radio-frequency drive used in the QCDD scheme, showing that, in the presented realization, its contribution to the systematic relative frequency uncertainty is below 10^{-17}, with the potential for further improvement. These results provide a promising avenue toward implementing multi-ion clocks exhibiting an order of magnitude or more improvement in stability while maintaining a similar high degree of accuracy to that of single-ion clocks.