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 measured the ground-state hyperfine splitting of trapped 113 C d + ions to be 15199862855.02799(27) Hz with a fractional uncertainty of 1.8 × 10 − 14 . The ions were trapped and laser-cooled in a linear quadrupole Paul trap. The fractional frequency stability was measured to be 4.2 × 10 − 13 / τ , obtained from Ramsey fringes of high signal-to-noise ratios and taken over a measurement time of nearly 5 h, which is close to the short-term stability limit estimated from the Dick effect. Our result is consistent with previously reported values, but the measurement precision is four times better than the best result obtained to date.

We report on the development of a microwave frequency standard based on a laser-cooled 171 Y b   +   ion trap system. The electronics , lasers, and magnetic shields are integrated into a single physical package. With over 105 ions are stably trapped, the system offers a high signal-to-noise ratio Ramsey line-shape. In comparison with previous work, the frequency instability of a 171 Y b   +   microwave clock was further improved to 8.5 × 10 − 13 / τ for averaging times between 10 and 1000 s. Essential systematic shifts and uncertainties are also estimated.

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 secondorder Doppler shifts was estimated to a level of 2 × 10 −17 . Up to 4.2 × 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) × 10 −17 using a high-accuracy 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.

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