${}^{174}{\mathrm{Y}\mathrm{b}}^{+}$-${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ sympathetic-cooling bi-species Coulomb crystal applied to microwave frequency standard

We reported the realization of a ${}^{174}{\mathrm{Y}\mathrm{b}}^{+}$-${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ bi-species Coulomb crystal comprising ${}^{174}{\mathrm{Y}\mathrm{b}}^{+}$ ions as coolant and verified its potential for application as a ${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ microwave frequency standard employing sympathetic cooling.The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The ${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the ${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to $5\times {10}^{-16}$, which represents an order of magnitude improvement over sympathetic cooled ${}^{40}{\mathrm{C}\mathrm{a}}^{+}$-${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ crystal. The uncertainty from the second-order Zeeman effect, which contributes the largest uncertainty to the microwave-ion frequency standard, is reduced to $4\times {10}^{-16}$. The relevant AC Stark shift uncertainty is estimated to be $4\times {10}^{-19}$. These results indicate using ${}^{174}{\mathrm{Y}\mathrm{b}}^{+}$ as coolant ions for ${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a ${}^{174}{\mathrm{Y}\mathrm{b}}^{+}$-${}^{113}{\mathrm{C}\mathrm{d}}^{+}$ two-component crystal.