Sympathetic cooling of ${}^{113}$Cd${}^{+}$ by laser-cooled ${}^{40}$Ca${}^{+}$ in a linear Paul trap for Microwave Ion Clocks

Abstract

We report sympathetic cooling of ${}^{113}$Cd${}^{+}$ by laser-cooled ${}^{40}$Ca${}^{+}$ in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of ${}^{113}$Cd${}^{+}$ ions was achieved. The temperature of these ions was measured at $90(10)$ mK, and the corresponding uncertainty arising from the second-order Doppler shifts was estimated to a level of $2\times 10^{-17}$. Up to $4.2\times 10^5$ Cd${}^{+}$ ions were confined in the trap, and the confinement time constant was measured to be 84 hours. After three hours of confinement, there were still $10^5$ Cd${}^{+}$ ions present, indicating that this Ca${}^{+}$--Cd${}^{+}$ dual ion system is surprisingly stable. The ac Stark shift was induced by the Ca${}^{+}$ lasers and fluorescence, which was carefully estimated to an accuracy of $5.4(0.5)\times 10^{-17}$ using a high-accuracy \textit{ab initio} approach. The Dick-effect-limited Allan deviation was also deduced because deadtimes were shorter. These results indicate that a microwave clock based on this sympathetic cooling scheme holds promise in providing ultra-high frequency accuracy and stability.