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.
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 ) .
Abstract Here we present a liquid nitrogen-cooled Ca+ optical clock with an overall systematic uncertainty of 3×10-18. In contrast with the room-temperature Ca+ optical clock that we have reported previously, the temperature of the blackbody radiation (BBR) shield in vacuum has been reduced to 82(5) K using liquid nitrogen. An ion trap with a lower heating rate and improved cooling lasers were also introduced. This allows cooling the ion temperature to the Doppler cooling limit during the clock operation, and the systematic uncertainty due to the ion’s secular (thermal) motion is reduced to < 1×10-18. The uncertainty due to the probe laser light shift and the servo error are also reduced to < 1×10-19 and 4×10-19 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 was measured with a fractional statistical uncertainty of 7×10-18. The differential BBR shift was used to calculate the static differential polarizability, and it was found in excellent agreement with our previous measurement with a different method. This work suggests that the BBR shift of optical clocks can be well suppressed in a liquid nitrogen environment. This is advantageous because conventional liquid-helium cryogenic systems for optical clocks are more expensive and complicated. Moreover, the proposed system can be used to suppress the BBR shift significantly in other types of optical clocks such as Yb+, Sr+, Yb, Sr, etc.
We present a liquid-nitrogen-cooled 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 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 Yb+, Sr+, Yb, Sr, etc.
Frequency standards based on optical transitions between electronic states of trapped ions have reached uncertainties below 10−18 [1]. The Stark shift caused by room-temperature blackbody radiation (BBR) causes the largest correction for most high-performance optical clock. The systematic uncertainty of 171Yb+ clocks based on the 2S1/2 (F = 0) → 2D3/2 (F = 2) electric quadrupole (E2) and 2S1/2 (F = 0) → 2F7/2 (F = 3) electric octupole (E3) transitions is currently limited to 28×10−18 and 1.5×10−18, respectively, by the fractional accuracy of the differential polarizability Δαdc of approximately 2% [2]. In the scope of this thesis, a dual species clock based on 171Yb+ and 88Sr+ ions was set up, operated and evaluated, to overcome this barrier. Since Δαdc is known with a smaller fractional uncertainty of 0.04% for the 2S1/2 → 2D5/2 E2 transition of 88Sr+ [3], this allows for a transfer of Δαdc from 88Sr+ to 171Yb+ following a method proposed in [4]. The optical intensity of a laser is calibrated with the Stark shift it causes on the 88Sr+ clock transition, allowing for the determination of Δαdc of the 171Yb+ clock transitions. This allows for a reduction of the fractional uncertainty of Δαdc for both 171Yb+ clock transitions below 0.4% and clock operation on the E2 and E3 transition with a fractional BBR shift uncertainty of 0.84×10−18 and 0.24×10−18 is enabled, respectively. However the value of Δαdc determined in this thesis does not agree with [2], a fractional offset of approximately 14% is observed. To investigate this discrepancy further, Δαdc is measured in the same manner as in [2] for the 88Sr+ clock transition. The same offset of approximately 14% is found, calling the accuracy of at least one of these methods into question. Finally, the first optical frequency ratio ℛ between the 88Sr+ clock transition and the 171Yb+ E3 transition is measured. The fractional uncertainty of ℛ is 23×10−18. ℛ in combination with the absolute frequency of the E3 transition allows for the determination of the 88Sr+ absolute frequency νSr+ with an uncertainty limited by the caesium references. The value of νSr+ falls outside of the recommended range, but is corroborated by measurements of the same quantity by other institutes [5, 6]. [1] M. Marshall et al., Phys. Rev. Lett. 135, 033201 (2025) [2] N. Huntemann et al., Phys. Rev. Lett. 116, 063001 (2016) [3] T. Lindvall et al., Phys. Rev. Lett. 135, 043402 (2025) [4] M. D. Barrett et al., Phys. Rev. A 100, 043418 (2019) [5] C. Marceau et al., Metrologia 62.4, 045001 (2025) [6] T. Lindvall et al., Phys. Rev. Appl. 24, 044082 (2025)
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.
Direct comparison of multi-ion optical clocks based on 40Ca+ and 88Sr+
We report the first direct frequency comparison between two multi-ion optical clocks based on the S1/2 to D5/2 transition in \Ca and \Sr ions. Using linear chains of up to nine \Ca ions and six \Sr ions, we demonstrate improved stability as a function of the number of ions that are contributing to the laser frequency stabilization servo. The measured joint fractional frequency stability of the two clocks reaches 1.37(12)×10−15 at one second, placing an upper bound on the same stability of one of the clocks at 9.6(8)×10−16 in one second. We measured the frequency ratio of the two clocks to be RSr/Ca=1.082076536381896986(18), where the systematic uncertainty is primarily limited by the room temperature blackbody radiation. Our direct measurement represents an order of magnitude improvement compared to existing indirect frequency ratio measurements. Furthermore, by combining our results with recent absolute frequency measurements of the \Sr transition, referenced to a primary frequency standard, we refined the absolute frequency of the \Ca transition to νCa+=411042129776400.21(4) Hz, reducing its uncertainty by a factor of three. This study presents the first direct comparison between two multi-ion optical clocks, highlighting their significant potential for future applications in fundamental physics tests, geodesy, and precision metrology.