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Physical Review Applied

Liquid-Nitrogen-Cooled Ca + Optical Clock with Systematic Uncertainty of 3×10−18

Yao Huang, Baolin Zhang, Mengyan Zeng, Yanmei Hao, Zixiao Ma, Huaqing Zhang, Hua Guan, Zheng Chen, Miao Wang, Kelin Gao

Published Mar 15, 2022• 82 citations
Publisher

Abstract

We present a liquid-nitrogen-cooled $\mathrm{Ca}$${}^{+}$ optical clock with an overall systematic uncertainty of $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. In contrast to the room-temperature $\mathrm{Ca}$${}^{+}$ optical clock that we have reported previously, the cryogenic black-body radiation (BBR) shield in vacuum is cooled to $82\ifmmode\pm\else\textpm\fi{}5$ K using liquid nitrogen. We also implement an ion trap with a reduced heating rate and improved laser cooling. This allows the ion temperature to fall to the Doppler-cooling limit during the clock operation and the systematic uncertainty associated with the secular (thermal) motion of the ion is reduced to $<1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. The uncertainty arising from the probe laser light shift and the servo error is also reduced to $<1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ and $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ with the hyper-Ramsey method and the higher-order servo algorithm, respectively. By comparing the output frequency of the cryogenic clock to that of a room-temperature clock, the differential BBR shift between the two is determined with a fractional statistical uncertainty of $7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$. The differential BBR shift is used to calculate the static differential polarizability and the result is found to be in excellent agreement with our previous measurement using a different method. This work suggests that the BBR shift of optical clocks can be suppressed well in a liquid-nitrogen environment. Systems similar to what is presented here can also be used to suppress the BBR shift significantly in other types of optical clocks, such as $\mathrm{Yb}$${}^{+}$, $\mathrm{Sr}$${}^{+}$, $\mathrm{Yb}$, Sr, etc.

DOI
10.1103/physrevapplied.17.034041

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We report a single-ion optical clock based on the 4S_{1/2}→3D_{5/2} transition of the ^{40}Ca^{+} ion, operated in a liquid nitrogen cryogenic environment, achieving a total systematic uncertainty of 4.4×10^{-19}. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation, and 3D sideband cooling to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the ^{40}Ca^{+} clock transition to be 14.345(15) Hz/mT^{2}, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.
A liquid-nitrogen cryogenic 40Ca+ optical clock is presented that is designed to greatly reduce the blackbody radiation (BBR) shift. The ion trap, the electrodes and the in-vacuum BBR shield are installed under the liquid-nitrogen container, keeping the ions in a cryogenic environment at liquid-nitrogen temperature. Compared with the first design in our previous work, many improvements have been made to increase the performance. The liquid-nitrogen maintenance time has been increased by about three times by increasing the volume of the liquid-nitrogen container; the trap position recovery time after refilling the liquid-nitrogen container has been decreased more than three times by using a better fixation scheme in the liquid-nitrogen container; and the magnetic field noise felt by the ions has been decreased more than three times by a better design of the magnetic shielding system. These optimizations make the scheme for reducing the BBR shift uncertainty of liquid-nitrogen-cooled optical clocks more mature and stable, and develop a stable lock with a narrower linewidth spectrum, which would be very beneficial for further reducing the overall systematic uncertainty of optical clocks.
Towards a transportable Ca+^++ optical clock with a systematic uncertainty of 4.8×10−184.8\times 10^{-18}4.8×10−18
We present a compact, long-term nearly continuous operation of a room-temperature Ca+^++ optical clock setup towards a transportable clock, achieving an overall systematic uncertainty of 4.8×10−184.8\times 10^{-18}4.8×10−18 and an uptime rate of 97.8% over an 8-day period. The active liquid-cooling scheme is adopted, combined with the precise temperature measurement with 13 temperature sensors both inside and outside the vacuum chamber to ensure the accurate evaluation of the thermal environment for the optical clock. The environmental temperature uncertainty is evaluated as 293.31(0.4) K, corresponding to a blackbody radiation (BBR) frequency shift uncertainty of 4.6×10−184.6\times 10^{-18}4.6×10−18, which is reduced more than two times compared to our previous work. Through the frequency comparison between the room temperature Ca+^++ optical clock and a cryogenic Ca+^++ optical clock, the overall uncertainty of the clock comparison is 7.5×10−187.5\times 10^{-18}7.5×10−18, including a statistic uncertainty of 4.9×10−184.9\times 10^{-18}4.9×10−18 and a systematic uncertainty of 5.7×10−185.7\times 10^{-18}5.7×10−18. This work provides a set of feasible implementations for high-precision transportable ion optical clocks.
We recently reported a 5×10-17level frequency comparison of two40Ca+optical clocks, one of which has fractional frequency uncertainty of 3.4×10-17, limited by the BBR effect. Here we present progress towards a40Ca+optical clock with uncertainty at the 10-18level. The differential static scalar polarizability Δα0 of the40Ca+ion clock transition is obtained by precisely measuring the “magic” rf drive frequency. Δα0 is measured as -7.2653(44)x10-40J m2/V2, the blackbody radiation shift is then calculated to be 0.3790(2) Hz at 300 K. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature is reduced to 5.6×10-19, the excess micromotion induced clock uncertainty is also reduced to the 10-19level by choosing the appropriate trap drive frequency. With a suppression of the BBR field temperature uncertainty to the sub-Kelvin level and improved clock stability, a robust, relatively low-cost40Ca+ion clock with uncertainty at 10-18level can be made.
Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .