The precision of Cadmium ion microwave clock based on linear quadrupole trap is mainly determined by the measurement accuracy of hyperfine splitting of the ground state of113Cd+. To reduce the second order Doppler frequency shift(SODFS), which is one of the main frequency shifts, we take advantages of sympathetic cooling by24Mg+ions to keep the Cadmium ion clouds at relatively low temperature during the interrogation of clock transition. By comparing the experiment results with molecular-dynamics(MD) simulation, we discuss the efficiency of sympathetic cooling and its influence on our clock's performance.
Abstract As a candidate for the next generation microwave clock, microwave atomic clocks based on trapped ions are currently studied worldwide. Since 2010, our team at Tsinghua University has been committed to developing a high-performance 113Cd+ microwave ion clock. In 2021, the laser-cooled cadmium-ion microwave clock constructed in our laboratory demonstrated remarkable performance, with a short-term instability of 4.2 × 10 − 13 / τ and a relative frequency uncertainty of 1.8 × 10−14, improving nearly three orders of magnitude compared to the result from JPL. The 0-0 ground-state hyperfine splitting frequency of 113Cd+ was determined to be 15199862855.02799(27) Hz, currently the most accurate measurement result for this transition frequency. Apart from that, we introduced the sympathetic cooling technology into the experiment of cadmium-ion microwave clock. Using 40Ca+ as the coolant ion, we obtained Ramsey patterns with a free evolution time of up to 100 seconds, ultimately improving the short-term instability of the system to 3.48 × 10 − 13 / τ . Moreover, a microwave frequency standard based on laser-cooled 171Yb+ ions has also been developed in our laboratory since 2021. The short-term frequency instability was measured to be 8.5 × 10 − 13 / τ . The ground-state hyperfine splitting frequency of 171Yb+ was determined to be 12642812118.4674(8) Hz with a fractional frequency uncertainty of 6.33 × 10−14.
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.