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.
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.
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.
A microwave frequency standard based on113Cd+ions at Tsinghua University has been carried out for twelve years. To overcome the limitations of the Dick effect and the second-order Doppler frequency shift (SODFS), we propose to use heavy174Yb+as the coolant ions to sympathetically cool the large113Cd+cloud, which is expected to further improve the performance of the cadmium-ion microwave frequency standard. This paper reports our recent experimental and simulation progress towards the cadmium-ion microwave frequency standard.
This paper reports direct temperature determination of sympathetically cooled 113Cd+ ions with laser-cooled 24Mg+ in a linear Paul trap. The sympathetically cooled ion species distribute in the outer shell of the large ensembles, which contain up to 3.3 × 105 ions. With optimized parameters, the minimum temperature of the sympathetically cooled 113Cd+ ions was measured to be on the order of 10 mK. These results are promising for the performance of microwave atomic clocks. The second-order Doppler frequency shift is two orders of magnitude lower (from 1.88 × 10−14 to 6.26 × 10−16) and the Dick effect is suppressed.