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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 (
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.-
Keywords:
- Ca+ ion optical clock /
- cryogenic /
- secular motion /
- excess micromotion
[1] Chen J 2009 Chin. Sci. Bull. 54 348
Google Scholar
[2] Dimarcq N, Gertsvolf M, Mileti G, Bize S, Oates C W, Peik E, Calonico D, Ido T, Tavella P, Meynadier F, Petit G, Panfilo G, Bartholomew J, Defraigne P, Donley E A, Hedekvist P O, Sesia I, Wouters M, Dubé P, Fang F, Levi F, Lodewyck J, Margolis H S, Newell D, Slyusarev S, Weyers S, Uzan J P, Yasuda M, Yu D H, Rieck C, Schnatz H, Hanado Y, Fujieda M, Pottie P E, Hanssen J, Malimon A, Ashby N 2024 Metrologia 61 012001
Google Scholar
[3] Riehle F, Gill P, Arias F, Robertsson L 2018 Metrologia 55 188
Google Scholar
[4] Gill P 2016 J. Phys. Conf. Ser. 723 012053
Google Scholar
[5] Takano T, Takamoto M, Ushijima I, Ohmae N, Akatsuka T, Yamaguchi A, Kuroishi Y, Munekane H, Miyahara B, Katori H 2016 Nat. Photonics 10 662
Google Scholar
[6] Schuldt T, Gohlke M, Oswald M, Wüst J, Blomberg T, Döringshoff K, Bawamia A, Wicht A, Lezius M, Voss K, Krutzik M, Herrmann S, Kovalchuk E, Peters A, Braxmaier C 2021 GPS Solutions 25 83
Google Scholar
[7] Takamoto M, Ushijima I, Ohmae N, Yahagi T, Kokado K, Shinkai H, Katori H 2020 Nat. Photonics 14 411
Google Scholar
[8] Sanner C, Huntemann N, Lange R, Tamm C, Peik E, Safronova M S, Porsev S G 2019 Nature 567 204
Google Scholar
[9] Mehlstäubler T E, Grosche G, Lisdat C, Schmidt P O, Denker H 2018 Rep. Prog. Phys. 81 064401
Google Scholar
[10] Gilmore K A, Affolter M, Lewis-Swan R J, Barberena D, Jordan E, Rey A M, Bollinger J J 2021 Science 373 673
Google Scholar
[11] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S, Peik E 2014 Phys. Rev. Lett. 113 210802
Google Scholar
[12] Chou C W, Hume D B, Rosenband T, Wineland D J 2010 Science 329 1630
Google Scholar
[13] Filzinger M, Dörscher S, Lange R, Klose J, Steinel M, Benkler E, Peik E, Lisdat C, Huntemann N 2023 Phys. Rev. Lett. 130 253001
Google Scholar
[14] Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Walsworth R L, Ye J 2016 Phys. Rev. D 94 124043
Google Scholar
[15] McGrew W F, Zhang X, Fasano R J, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H, Ludlow A D 2018 Nature 564 87
Google Scholar
[16] Aeppli A, Kim K, Warfield W, Safronova M S, Ye J 2024 Phys. Rev. Lett. 133 023401
Google Scholar
[17] Ma Z Y, Deng K, Wang Z Y, Wei W Z, Hao P, Zhang H X, Pang L R, Wang B, Wu F F, Liu H L, Yuan W H, Chang J L, Zhang J X, Wu Q Y, Zhang J, Lu Z H 2024 Phys. Rev. Appl. 21 044017
Google Scholar
[18] Li J, Cui X Y, Jia Z P, Kong D Q, Yu H W, Zhu X Q, Liu X Y, Wang D Z, Zhang X, Huang X Y, Zhu M Y, Yang Y M, Hu Y, Liu X P, Zhai X M, Liu P, Jiang X, Xu P, Dai H N, Chen Y A, Pan J W 2024 Metrologia 61 015006
Google Scholar
[19] Ushijima I, Takamoto M, Das M, Ohkubo T, Katori H 2015 Nat. Photonics 9 185
Google Scholar
[20] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
Google Scholar
[21] Huang Y, Zhang B, Zeng M, Hao Y, Ma Z, Zhang H, Guan H, Chen Z, Wang M, Gao K 2022 Phys. Rev. Appl. 17 034041
Google Scholar
[22] Tofful A, Baynham C F A, Curtis E A, Parsons A O, Robertson B I, Schioppo M, Tunesi J, Margolis H S, Hendricks R J, Whale J, Thompson R C, Godun R M 2024 Metrologia 61 045001
Google Scholar
[23] Lu B K, Sun Z, Yang T, Lin Y G, Wang Q, Li Y, Meng F, Lin B K, Li T C, Fang Z J 2022 Chin. Phys. Lett. 39 080601
Google Scholar
[24] Zhiqiang Z, Arnold K J, Kaewuam R, Barrett M D 2023 Sci. Adv. 9 eadg1971
Google Scholar
[25] Lu X, Guo F, Wang Y, Xu Q, Zhou C, Xia J, Wu W, Chang H 2023 Metrologia 60 015008
Google Scholar
[26] Arnold K J, Kaewuam R, Roy A, Tan T R, Barrett M D 2018 Nat. Commun. 9 1650
Google Scholar
[27] Dubé P, Madej A A, Tibbo M, Bernard J E 2014 Phys. Rev. Lett. 112 173002
Google Scholar
[28] Huang Y, Guan H, Zeng M, Tang L, Gao K 2019 Phys. Rev. A 99 011401
Google Scholar
[29] Porsev S G, Derevianko A 2006 Phys. Rev. A 74 020502
Google Scholar
[30] Angstmann E J, Dzuba V A, Flambaum V V 2006 Phys. Rev. Lett. 97 040802
Google Scholar
[31] Zeng M, Huang Y, Zhang B, Hao Y, Ma Z, Hu R, Zhang H, Chen Z, Wang M, Guan H, Gao K 2023 Phys. Rev. Appl. 19 064004
Google Scholar
[32] Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004
Google Scholar
[33] Doležal M, Balling P, Nisbet-Jones P B R, King S A, Jones J M, Klein H A, Gill P, Lindvall T, Wallin A E, Merimaa M, Tamm C, Sanner C, Huntemann N, Scharnhorst N, Leroux I D, Schmidt P O, Burgermeister T, Mehlstäubler T E, Peik E 2015 Metrologia 52 842
Google Scholar
[34] Zeng M, Huang Y, Zhang B, Ma Z, Hao Y, Hu R, Zhang H, Guan H, Gao K 2023 Chin. Phys. B 32 113701
Google Scholar
[35] Berkeland D J, Miller J D, Bergquist J C, Itano W M, Wineland D J 1998 J. Appl. Phys. 83 5025
Google Scholar
[36] Chen J S, Brewer S M, Chou C W, Wineland D J, Leibrandt D R, Hume D B 2017 Phys. Rev. Lett. 118 053002
Google Scholar
[37] Keller J, Partner H L, Burgermeister T, Mehlstäubler T E 2015 J. Appl. Phys. 118 104501
Google Scholar
[38] Wineland D J, Monroe C, Itano W M, Leibfried D, King B E, Meekhof D M 1998 J. Res. Nat. Inst. Stand. Technol. 103 259
Google Scholar
[39] James D F V 1998 Appl. Phys. B 66 181
Google Scholar
[40] Zhang B, Huang Y, Hao Y, Zhang H, Zeng M, Guan H, Gao K 2020 J. Appl. Phys. 128 143105
Google Scholar
[41] Zhang B, Huang Y, Zhang H, Hao Y, Zeng M, Guan H, Gao K 2020 Chin. Phys. B 29 074209
Google Scholar
[42] Dubé P, Madej A A, Zhou Z, Bernard J E 2013 Phys. Rev. A 87 023806
Google Scholar
[43] Huntemann N, Sanner C, Lipphardt B, Tamm C, Peik E 2016 Phys. Rev. Lett. 116 063001
Google Scholar
[44] Chou C W, Hume D B, Koelemeij J C J, Wineland D J, Rosenband T 2010 Phys. Rev. Lett. 104 070802
Google Scholar
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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; (h) helical resonator; (i) soft copper wire; (j) insulating ceramic; (k) cap electrode; (l) PT100 resistance temperature detector; (m) trap base; (n) 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. 射频电势幅值的稳定通过偏置器(Bias Tee)、射频检波器以及信号源的幅度调制功能来实现. 蓝色方框区域表示主动反馈控制回路, 其工作原理是: 采集补偿电极上的射频感应电压, 经反馈回路处理后, 将射频驱动电压信号锁定, 并反馈至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 box indicates the active feedback control loop, which operates by detecting the RF-induced voltage on the compensation electrode, processing it through the feedback loop, and feeding it back to the amplitude modulation input of the RF signal generator to lock the RF drive voltage signal.
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. 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概率, 通过100次重复探测得到. 橘黄色虚线是对实验数据的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) 红边带和(b)蓝边带的跃迁谱线, 其中探测时间为20 μs, 红色和蓝色的圆点表示实验测得的跃迁概率, 对应的红色与蓝色实线是通过sinc函数对实验数据的拟合; (c) Doppler冷却后红蓝边带的Rabi振荡. 每个跃迁概率均通过200次重复实验得到
Figure 6. (a) Red and (b) 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) 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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[1] Chen J 2009 Chin. Sci. Bull. 54 348
Google Scholar
[2] Dimarcq N, Gertsvolf M, Mileti G, Bize S, Oates C W, Peik E, Calonico D, Ido T, Tavella P, Meynadier F, Petit G, Panfilo G, Bartholomew J, Defraigne P, Donley E A, Hedekvist P O, Sesia I, Wouters M, Dubé P, Fang F, Levi F, Lodewyck J, Margolis H S, Newell D, Slyusarev S, Weyers S, Uzan J P, Yasuda M, Yu D H, Rieck C, Schnatz H, Hanado Y, Fujieda M, Pottie P E, Hanssen J, Malimon A, Ashby N 2024 Metrologia 61 012001
Google Scholar
[3] Riehle F, Gill P, Arias F, Robertsson L 2018 Metrologia 55 188
Google Scholar
[4] Gill P 2016 J. Phys. Conf. Ser. 723 012053
Google Scholar
[5] Takano T, Takamoto M, Ushijima I, Ohmae N, Akatsuka T, Yamaguchi A, Kuroishi Y, Munekane H, Miyahara B, Katori H 2016 Nat. Photonics 10 662
Google Scholar
[6] Schuldt T, Gohlke M, Oswald M, Wüst J, Blomberg T, Döringshoff K, Bawamia A, Wicht A, Lezius M, Voss K, Krutzik M, Herrmann S, Kovalchuk E, Peters A, Braxmaier C 2021 GPS Solutions 25 83
Google Scholar
[7] Takamoto M, Ushijima I, Ohmae N, Yahagi T, Kokado K, Shinkai H, Katori H 2020 Nat. Photonics 14 411
Google Scholar
[8] Sanner C, Huntemann N, Lange R, Tamm C, Peik E, Safronova M S, Porsev S G 2019 Nature 567 204
Google Scholar
[9] Mehlstäubler T E, Grosche G, Lisdat C, Schmidt P O, Denker H 2018 Rep. Prog. Phys. 81 064401
Google Scholar
[10] Gilmore K A, Affolter M, Lewis-Swan R J, Barberena D, Jordan E, Rey A M, Bollinger J J 2021 Science 373 673
Google Scholar
[11] Huntemann N, Lipphardt B, Tamm C, Gerginov V, Weyers S, Peik E 2014 Phys. Rev. Lett. 113 210802
Google Scholar
[12] Chou C W, Hume D B, Rosenband T, Wineland D J 2010 Science 329 1630
Google Scholar
[13] Filzinger M, Dörscher S, Lange R, Klose J, Steinel M, Benkler E, Peik E, Lisdat C, Huntemann N 2023 Phys. Rev. Lett. 130 253001
Google Scholar
[14] Kolkowitz S, Pikovski I, Langellier N, Lukin M D, Walsworth R L, Ye J 2016 Phys. Rev. D 94 124043
Google Scholar
[15] McGrew W F, Zhang X, Fasano R J, Schäffer S A, Beloy K, Nicolodi D, Brown R C, Hinkley N, Milani G, Schioppo M, Yoon T H, Ludlow A D 2018 Nature 564 87
Google Scholar
[16] Aeppli A, Kim K, Warfield W, Safronova M S, Ye J 2024 Phys. Rev. Lett. 133 023401
Google Scholar
[17] Ma Z Y, Deng K, Wang Z Y, Wei W Z, Hao P, Zhang H X, Pang L R, Wang B, Wu F F, Liu H L, Yuan W H, Chang J L, Zhang J X, Wu Q Y, Zhang J, Lu Z H 2024 Phys. Rev. Appl. 21 044017
Google Scholar
[18] Li J, Cui X Y, Jia Z P, Kong D Q, Yu H W, Zhu X Q, Liu X Y, Wang D Z, Zhang X, Huang X Y, Zhu M Y, Yang Y M, Hu Y, Liu X P, Zhai X M, Liu P, Jiang X, Xu P, Dai H N, Chen Y A, Pan J W 2024 Metrologia 61 015006
Google Scholar
[19] Ushijima I, Takamoto M, Das M, Ohkubo T, Katori H 2015 Nat. Photonics 9 185
Google Scholar
[20] Brewer S M, Chen J S, Hankin A M, Clements E R, Chou C W, Wineland D J, Hume D B, Leibrandt D R 2019 Phys. Rev. Lett. 123 033201
Google Scholar
[21] Huang Y, Zhang B, Zeng M, Hao Y, Ma Z, Zhang H, Guan H, Chen Z, Wang M, Gao K 2022 Phys. Rev. Appl. 17 034041
Google Scholar
[22] Tofful A, Baynham C F A, Curtis E A, Parsons A O, Robertson B I, Schioppo M, Tunesi J, Margolis H S, Hendricks R J, Whale J, Thompson R C, Godun R M 2024 Metrologia 61 045001
Google Scholar
[23] Lu B K, Sun Z, Yang T, Lin Y G, Wang Q, Li Y, Meng F, Lin B K, Li T C, Fang Z J 2022 Chin. Phys. Lett. 39 080601
Google Scholar
[24] Zhiqiang Z, Arnold K J, Kaewuam R, Barrett M D 2023 Sci. Adv. 9 eadg1971
Google Scholar
[25] Lu X, Guo F, Wang Y, Xu Q, Zhou C, Xia J, Wu W, Chang H 2023 Metrologia 60 015008
Google Scholar
[26] Arnold K J, Kaewuam R, Roy A, Tan T R, Barrett M D 2018 Nat. Commun. 9 1650
Google Scholar
[27] Dubé P, Madej A A, Tibbo M, Bernard J E 2014 Phys. Rev. Lett. 112 173002
Google Scholar
[28] Huang Y, Guan H, Zeng M, Tang L, Gao K 2019 Phys. Rev. A 99 011401
Google Scholar
[29] Porsev S G, Derevianko A 2006 Phys. Rev. A 74 020502
Google Scholar
[30] Angstmann E J, Dzuba V A, Flambaum V V 2006 Phys. Rev. Lett. 97 040802
Google Scholar
[31] Zeng M, Huang Y, Zhang B, Hao Y, Ma Z, Hu R, Zhang H, Chen Z, Wang M, Guan H, Gao K 2023 Phys. Rev. Appl. 19 064004
Google Scholar
[32] Bothwell T, Kedar D, Oelker E, Robinson J M, Bromley S L, Tew W L, Ye J, Kennedy C J 2019 Metrologia 56 065004
Google Scholar
[33] Doležal M, Balling P, Nisbet-Jones P B R, King S A, Jones J M, Klein H A, Gill P, Lindvall T, Wallin A E, Merimaa M, Tamm C, Sanner C, Huntemann N, Scharnhorst N, Leroux I D, Schmidt P O, Burgermeister T, Mehlstäubler T E, Peik E 2015 Metrologia 52 842
Google Scholar
[34] Zeng M, Huang Y, Zhang B, Ma Z, Hao Y, Hu R, Zhang H, Guan H, Gao K 2023 Chin. Phys. B 32 113701
Google Scholar
[35] Berkeland D J, Miller J D, Bergquist J C, Itano W M, Wineland D J 1998 J. Appl. Phys. 83 5025
Google Scholar
[36] Chen J S, Brewer S M, Chou C W, Wineland D J, Leibrandt D R, Hume D B 2017 Phys. Rev. Lett. 118 053002
Google Scholar
[37] Keller J, Partner H L, Burgermeister T, Mehlstäubler T E 2015 J. Appl. Phys. 118 104501
Google Scholar
[38] Wineland D J, Monroe C, Itano W M, Leibfried D, King B E, Meekhof D M 1998 J. Res. Nat. Inst. Stand. Technol. 103 259
Google Scholar
[39] James D F V 1998 Appl. Phys. B 66 181
Google Scholar
[40] Zhang B, Huang Y, Hao Y, Zhang H, Zeng M, Guan H, Gao K 2020 J. Appl. Phys. 128 143105
Google Scholar
[41] Zhang B, Huang Y, Zhang H, Hao Y, Zeng M, Guan H, Gao K 2020 Chin. Phys. B 29 074209
Google Scholar
[42] Dubé P, Madej A A, Zhou Z, Bernard J E 2013 Phys. Rev. A 87 023806
Google Scholar
[43] Huntemann N, Sanner C, Lipphardt B, Tamm C, Peik E 2016 Phys. Rev. Lett. 116 063001
Google Scholar
[44] Chou C W, Hume D B, Koelemeij J C J, Wineland D J, Rosenband T 2010 Phys. Rev. Lett. 104 070802
Google Scholar
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