Characteristics of secular- and excess micro-motion of a liquid nitrogen-cooled Ca<sup>+</sup> ion optical clock

MA Zixiao; ZHANG Baolin; HUANG Yao; GAO Kelin; GUAN Hua

doi:10.7498/aps.74.20250048

Abstract

In ion optical clock systems, the motional effect of trapped ions is a key factor determining clock performance and currently representing a key limitation in achieving lower uncertainty between different ion-based optical clocks. According to the first liquid nitrogen-cooled Ca⁺ ion optical clock (2022 Phys. Rev. Appl. 17 034041), we develop a new physical system for a second Ca⁺ ion optical clock and make significant improvements to its ion trapping apparatus. These improvements primarily focus on two aspects. The first aspect is that we design and implement an active stabilization system for the RF voltage, which stabilizes the induced radio-frequency (RF) signal on the compensation electrodes by adjusting the amplitude of the RF source in real time. This method effectively suppresses long-term drifts in the radial secular motion frequencies to less than 1 kHz, achieving stabilized values of $\omega_x = 2\pi \times 3.522(2)\;\mathrm{MHz}$ and $\omega_y = 2\pi \times 3.386(2)\;\mathrm{MHz}$. The induced RF signal is stabilized at 59121.43(12) µV, demonstrating the high precision of the stabilization system. The second aspect is that we optimize the application of compensation voltages by directly integrating the vertical compensation electrodes into an ion trap structure. This refinement can suppress excess micromotion in all three mutually orthogonal directions to an even lower level. Tuning the RF trapping frequency close to the magic trapping condition of the clock transition, we further evaluate the excess micromotion-induced frequency shift in the optical clock to be $2(1) \times 10^{-19}$. To quantitatively assess the secular-motion of the trapped ion, we measure the sideband spectra on the radial and axial motion modes, both red and blue sideband spectra. From these measurements, we accurately determine the mean phonon number in the three motional modes after Doppler cooling, corresponding to an average ion temperature of $0.78(39)\;\mathrm{mK}$, which is close to the Doppler cooling limit. The corresponding second-order Doppler shift is evaluated to be $-(2.71 \pm 1.36) \times 10^{-18}$. The long-term stability of the radial secular motion frequency provides favorable conditions for implementing three-dimensional sideband cooling in future experiments, which will further reduce the second-order Doppler shift. These advancements not only enhance the overall stability of the optical clock but also lay the foundation for reducing its systematic uncertainty to the $10^{-19}$ level.

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Corresponding author: HUANG Yao, yaohuang@apm.ac.cn ; GUAN Hua, guanhua@apm.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant Nos. 2022YFB3904001, 2022YFB3904004), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0300901), the National Natural Science Foundation of China (Grant Nos. 12204494, 12121004, 12320101003, 11934014), and the Natural Science Foundation of Hubei Province, China (Grant Nos. 2023EHA006, 2022CFA013).

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Vol. 74, Issue 9 - 2025-05-05

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