We reported the realization of a 174Yb+–113Cd+ bi-species Coulomb crystal comprising 174Yb+, a heavier ion, as coolant and verified the potential of applying a coolant ion with a greater mass than the clock ion to sympathetically cooled microwave frequency standard. The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micro-motion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+–113Cd+ crystal. The second-order Zeeman frequency shift, which contributes the largest term of the systematic frequency shifts to the microwave ion frequency standard, is estimated to be as low as 7.133×10−13 corresponding to the low value of the operating magnetic field. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results demonstrate that using a heavier coolant ion is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+–113Cd+ bicrystal.
We report a high-performance transportable microwave frequency standard scheme based on sympathetically cooled 113Cd+ ions using 40Ca+ as coolant ions. A transportable physical package (1.4 m3) with high-performance magnetic shielding (radial shielding coefficient 460 000) has been built. In experiments, more than 105 113Cd+ ions were sympathetically cooled to 90 mK in a Paul trap and the ion-loss time constant extends to 84 hours. Without direct cooling procedures, the Dick effect-limited Allan deviation due to the deadtimes is reduced to 1.8×10−14/τ. Under our scheme, the uncertainties in the main frequency shifts such as those from second-order Zeeman and second-order Doppler terms were reduced below the order of 10−15. The relevant ac Stark shifts uncertainties were estimated to be below 5×10−18. Minor shifts further reflect the superiority of coolant ions 40Ca+ for 113Cd+. These results indicate that a microwave clock based on this sympathetic cooling scheme shows potential in establishing a vehicle transportable ground-based time-frequency reference for navigation systems.
We report sympathetic cooling of
113Cd
+ by laser-cooled
40Ca
+ in a linear Paul trap for microwave clocks. Long-term low-temperature confinement of
113Cd
+ 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
2×10−17. Up to
4.2×105 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
105 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)×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.
We reported the realization of a
174Yb+-
113Cd+ bi-species Coulomb crystal comprising
174Yb+ ions as coolant and verified its potential for application as a
113Cd+ 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
113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micromotion to which the
113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to
5×10−16, which represents an order of magnitude improvement over sympathetic cooled
40Ca+-
113Cd+ crystal. The uncertainty from the second-order Zeeman effect, which contributes the largest uncertainty to the microwave-ion frequency standard, is reduced to
4×10−16. The relevant AC Stark shift uncertainty is estimated to be
4×10−19. These results indicate using
174Yb+ as coolant ions for
113Cd+ is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a
174Yb+-
113Cd+ two-component crystal.
The ion microwave frequency standard is a candidate for the next generation of microwave frequency standard with the potential for very wide applications. The Dick effect and second-order Doppler frequency shift (SODFS) limit the performance of ion microwave frequency standards. The introduction of sympathetic cooling technology can suppress the Dick effect and SODFS and improve the stability and accuracy of the frequency standard. However, the sympathetically cooled ion microwave frequency standard has seldom been studied before. This paper reports a high-performance sympathetically cooled ion microwave frequency standard in a Paul trap. Using laser-cooled
40Ca+ as coolant ions,
113Cd+ ion crystal is cooled to below 100 mK and has a coherence lifetime of over 40 s. The short-term frequency stability reached $3.48\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/{\ensuremath{\tau}}^{1/2}$, which is comparable to that of the mercury ion frequency standard. Its uncertainty is $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$, which is better than that of directly laser-cooled cadmium ion frequency standard.