A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator. Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10−18, which is meaningful for the systematic uncertainty of the transportable single 40Ca+ ion optical clock entering the 10−18 level.
A universal locking model for single ion optical clocks was built based on a simple integrator and a double integrator. Different integrator algorithm parameters have been analyzed in both numerical simulations and experiments. The frequency variation measured by the comparison of two optical clocks coincides well with the simulation results for different second integrator parameters. According to the experimental results, the sensitivity of the servo error influenced by laser frequency drift with the addition of a double integrator was suppressed by a factor of 107. In a week-long comparison of optical clocks, the relative uncertainty of the servo error is determined to be 1.9 × 10−18, which is meaningful for the systematic uncertainty of the transportable single 40Ca+ ion optical clock entering the 10−18 level.
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 ) .
A fundamental limit to the stability of a single-ion optical frequency standard is set by quantum noise in the measurement of the internal state of the ion. We discuss how the interrogation sequence and the processing of the atomic resonance signal can be optimized in order to obtain the highest possible stability under realistic experimental conditions. A servo algorithm is presented that stabilizes a laser frequency to the single-ion signal and that eliminates errors due to laser frequency drift. Numerical simulations of the servo characteristics are compared to experimental data from a frequency comparison of two single-ion standards based on a transition at 688 THz in 171 Yb + . Experimentally, an instability σ y (100 s) = 9 × 10 −16 is obtained in the frequency difference between both standards.
We report a robust, compact, and transportable optical clock (TOC-729-2) based on a trapped single 40Ca+ ion with a systematic uncertainty of 1.1×10−17, which is limited by the black-body radiation shift uncertainty at room temperature. By comparing it with the previous transportable optical clock (TOC-729-1) similar but completely independent, the instability was measured to be better than 1.2×10−14/τ. Benefiting from the modular and integrated design, this TOC was constructed in a volume of ∼0.33 m3 excluding the controlling electronics in 19-in. racks. After being moved ∼1200 km away by express delivery, the single-ion signal was restored within 24 h. With the TOC uptime of 92% in 35-day period, the absolute frequency of the 729 nm transition of 40Ca+ was measured using a satellite link to International Atomic Time (TAI) to provide traceability to the SI second, and the result is 411 042 129 776 400.15(22) Hz, corresponding to a relative uncertainty of 5.3×10−16.
A multi-ion optical clock with 5×10−19 uncertainty
Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below 1×10−18. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of 5.3×10−19 and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the 10−20-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of 0.6926711632159660405(20), with a statistical uncertainty of 0.9×10−18 and a combined uncertainty of 2.9×10−18. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.
Based on the current initiative to redefine the SI “second”, the optical clock has been demonstrated by many laboratories as a favorable candidate due to its excellent performance indicators. We describe the evaluation of uncertainty and optimization of stability in an aluminum-ion optical clock system based on quantum logic spectroscopy. The uncertainty evaluation of the current optical clock system is1.6×10−18. The frequency stability of a single system has been improved from 3.9×10−15/τto 2.6×10−15/τby using the servo-controlled self-comparison locking method.
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.