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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 [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 59 121.43(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 macro-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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Keywords:
- Ca+ ion optical clock /
- cryogenic /
- secular motion /
- excess micromotion
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图 1 新建低温系统离子阱部分装置图. 显著特征包括: (a) 液氮入口; (b) 不锈钢真空壁; (c) 高纯无氧铜液氮桶; (d) 射频电极馈通; (e) 黑体辐射屏蔽腔; (f) 观察窗; (g) 离子阱; (h) 谐振器; (i) 软铜导线; (j) 绝缘陶瓷; (k) 帽电极; (l) PT100测温探头; (m) 离子阱底座; (n) 电压传输钢丝. 离子阱左侧的其中一对电极上接交流信号, 右侧的两个直流电极用于离子的水平方向及竖直方向的补偿
Figure 1. Schematic of the ion trap section in the newly developed low-temperature system. Key features include: (a) Liquid nitrogen inlet; (b) Stainless steel vacuum chamber; (c) Oxygen-free high copper(OFHC) liquid nitrogen container; (d) RF electrode feedthrough; (e) Blackbody radiation shielding chamber; (f) Viewports; (g) Ion trap; (g) Helical resonator; (h) Soft copper wire; (i) Insulating ceramic; (j) Cap electrode; (k) PT100 Resistance Temperature Detector; (l) Trap base; (m) Voltage transmission steel wire. One pair of electrodes on the left side of the ion trap is connected to an AC signal, while the two DC electrodes on the right side are used for compensation in the horizontal and vertical directions of the ions.
图 2 射频电压主动稳定装置系统框图. 稳定射频电势幅值通过偏置器Bias Tee、射频检波器及信号源的幅度调制功能实现, 蓝色方框区域包含了主动反馈的控制回路, 通过采集补偿电极上的射频感应电压并通过反馈回路将射频驱动电压信号锁定并反馈给射频信号源的幅度调制端口
Figure 2. Block Diagram of the Active RF Voltage Stabilization System. The stabilization of the RF potential amplitude is achieved using a bias tee, an RF detector, and the amplitude modulation function of the signal source. The blue-boxed region represents the active feedback control loop, which monitors the RF-induced voltage on the compensation electrode and feeds it back to the amplitude modulation port of the RF signal source, thereby locking the RF drive voltage.
图 3 射频电压主动稳定装置的实验效果. (a)、(c)、(e) 与 (g) 分别显示了在稳压电路未开启时宏运动频率与感应信号幅值的变化情况, 径向的宏运动频率与感应信号的变化一致; (b)、(d)、(f) 与 (h) 分别为稳压电路开启时的宏运动频率与感应信号幅值的变化情况
Figure 3. The measurement results of the secular frequency and induced voltage. (a), (c), (e), and (g) show the variations in motional frequencies and induced signal amplitudes when the stabilization circuit is off, where the changes in radial motional frequencies are consistent with those in the induced signals. (b), (d), (f), and (h) present the corresponding variations when the stabilization circuit is on.
图 4 第一代(左侧)和第二代(右侧)液氮低温光钟的离子囚禁装置示意图
Figure 4. Schematic comparison of the ion trap devices used in the first-generation (left) and the improved second-generation (right) liquid nitrogen cooled optical clocks.
图 5 三维正交方向上载波与微运动边带的Rabi振荡. 图中圆点为实验测得的跃迁几率, 通过100次重复探测得到. 橘黄色实线是对实验数据的sin函数拟合
Figure 5. Rabi oscillations of the carrier and micromotion sidebands along three orthogonal directions. The dots represent the experimentally measured transition probabilities, obtained by averaging 100 repeated measurements. The orange curve is a sinusoidal fit to the experimental data.
图 6 (a) 和 (b) 分别为红边带和蓝边带的跃迁谱线. 探测时间为20 us, 红色和蓝色的圆点表示实验测得的跃迁几率, 对应的红色与蓝色的实线是通过sinc函数对实验数据的拟合. (c)为Doppler冷却后红蓝边带的Rabi振荡. 每个跃迁几率均通过200次重复实验得到
Figure 6. (a) and (b) show the red and blue sideband transition spectra, respectively, with an interrogation time of 20 µs for per measurement. The red and blue dots represent the experimentally measured transition probabilities, while the corresponding red and blue curves are sinc function fits to the data. (c) shows the Rabi oscillations of the red and blue sidebands after Doppler cooling. Each data point represents the average transition probability obtained from 200 repeated measurements.
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