Toward a high-performance transportable microwave frequency standard based on sympathetically cooled 113Cd+ ions

Abstract

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.

Sympathetic cooling of a large ${}^{113}\mathrm{Cd}^{+}$ ion crystal with ${}^{40}\mathrm{Ca}^{+}$ in a linear Paul trap

“…The experimental setup has been described in more detail elsewhere [29,30]; here, a brief description of the linear Paul trap suffices (Fig. 1).…”

“…In 2021, we replaced 24 Mg + with 40 Ca + as the coolant. Although the mass ratio of 0.354 between 40 Ca + and 113 Cd + limits the sympathetic cooling efficiency, sympathetic cooling of 113 Cd + ions was still preliminarily achieved [29]. However, the large two-component ion crystals in the Paul trap are still lacking in thorough research.…”

Determination of hyperfine splittings and Landé $g_J$ factors of $5s~^2S_{1/2}$ and $5p~^2P_{1/2,3/2}$ states of $^{111,113}$Cd$^+$ for a microwave frequency standard

“…Briefly, for the experimental setup (see Ref. [19] for details), we prepared crystals of two ion species consisting of approximately 10 5 Ca + and Cd + ions in a linear Paul trap. The Ca + and Cd + ions are produced by selected-photoionization using laser beams of wavelength 423-nm (Ca 4s 2 1 S 0 -4s4p 1 P 1 ) / 374-nm (Ca 4s4p 1 P 1 -Continuum), and 228-nm (Cd 5s 2 1 S 0 -5s5p 1 P 1 ).…”

“…2), the beam intensity is maintained below 5 µW/mm 2 (saturation parameter 0.0006) to reduce the cooling and heating effects of the probe beam. The fitted curve is the Voigt profile [19,26], expressed as…”

“…The high performance and potential for miniaturization make this frequency standard suitable in establishing a ground-based transportable frequency reference for navigation systems and for comparing atomic clocks between remote sites [15][16][17][18]. Moreover, it has been proposed as a means to achieve an ultra-high level of accuracy down to 10 −15 [19], highlighting the importance of accurately evaluating systematic frequency shifts.…”