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Journal of Applied Physics

Improvement in the stability of a 40Ca+ ion optical clock using the Ramsey method

Baolin Zhang, Yao Huang, Yanmei Hao, Huaqing Zhang, Mengyan Zeng, Hua Guan, Kelin Gao

Published Oct 14, 2020• 15 citations
Publisher

Abstract

The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2×10−17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3×10−15/τ to 2.5×10−15/τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5×10−17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.

DOI
10.1063/5.0012726

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The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2×10−17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3×10−15/τ to 2.5×10−15/τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5×10−17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.
In this review, the improvements made in the past two decades for 40Ca+ optical clocks in China are presented. Uncertainty of below 1.3×10−17 was achieved by applying the “magic” RF trapping frequency and introducing a generalized Ramsey excitation scheme. The stability of 40Ca+ optical clocks has been improved to 2.5×10−15/τ with an uptime rate of 93.8% by implementing two ameliorated lock algorithms in the Ramsey excitation scheme. A long-term clock frequency comparison shows a clock stability of 6.3 × 10−18 in an averaging time of 524 000 s. A robust and transportable clock installed in an air-conditioned car trailer can achieve almost the same performance of laboratory clocks. A height difference between transportable and laboratory clocks was measured with an uncertainty of 0.33 m and the absolute frequency of 40Ca+ optical clock transitions was remeasured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of 5.6×10−16 based on a Cs fountain clock in the National Institute of Metrology after the transportable clock was transported from Wuhan to Beijing. The author predicts that transportable single-ion optical clocks especially based on the 40Ca+ will make a significant contribution to the construction of a world-wide optical clock network and the redefinition of the unit of time in the future.
A number of optical frequency standards have been evaluated with fractional uncertainties between ${10}^{\ensuremath{-}17}$ and ${10}^{\ensuremath{-}18}$. Reduction of the statistical uncertainty of a clock comparison to this level is challenging, requiring the best possible stability to avoid excessively long averaging times. We report recent improvements of our 88Sr+^{88}\mathrm{Sr}{}^{+}88Sr+ single-ion standard that have reduced its 1-s Allan deviation from $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$, yielding an order of magnitude decrease in averaging time for a given statistical uncertainty level. Among the improvements made are the implementation of a clear-out laser that transfers the ion from the metastable state to the ground state at each cycle, followed by a state preparation step that transfers the ion to the ground-state magnetic sublevel of the probed transition. With these changes, the ion clock transition interacts with the probe laser at every interrogation cycle. The stability of our optical standard is essentially limited by the quantum projection noise for pulse lengths up to $\ensuremath{\approx}100$ ms.
Laser noise usually limits the stability of optical frequency ratio measurements, limiting the speed and precision one can compare two atomic frequency standards. In this talk I will describe two methods, correlation and differential spectroscopy, which utilize correlations in laser noise to increase the achievable interrogation time and thus increase the frequency comparison stability. Correlation spectroscopy is a technique which uses a parity measurement following a synchronized Ramsey interrogation to measure the relative frequency of two similar frequency atomic clocks. With this technique we achieve a measurement instability of (4×10^(-16))⁄√(τ⁄s) for a comparison of two single 27Al+ ion clocks. Differential spectroscopy uses an atomic clock with low projection noise, here a 171Yb lattice clock, to correct the phase noise of a second, higher frequency clock’s local oscillator thereby reducing the measurement instability to the level of the first. This can be further extended using two lattice clocks in a zero dead time configuration to correct the phase noise beyond the interrogation time reachable for a single Yb lattice clock. With these techniques we achieve measurement stabilities of (2.5×10^(-16))⁄√(τ⁄s) and (2×10^(-16))⁄√(τ⁄s) for a comparison between a single 27Al+ ion clock and a 171Yb lattice clock running as single clock and in a zero dead time configuration respectively. In addition to these techniques, I will also discuss recent progress towards characterizing the systematics of the NIST 40Ca+/27Al+ optical atomic clock.
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 develop a compact multilayer magnetic shield for a transportable optical clock, achieving shielding factors of up to 10 5 . To improve the frequency stability of the transportable optical clock, we improved the magnetic-field environment of a transportable 40 Ca + ion optical clock (TCIOC) using the newly developed magnetic shielding system and reduced the clock-laser frequency noise by transferring the stability of an ultrastable reference laser through an optical frequency comb. These improvements enabled the coherent interrogation time to be extended from 40 ms to 320 ms . A time-interleaved self-comparison yielded a measured short-term fractional frequency instability of 1.6 × 10 − 15 / τ , close to the estimated quantum projection noise-limited instability of 1.18 × 10 − 15 / τ . Meanwhile, the uncertainty contributions associated with the DC second-order Zeeman shift and the servo error were reduced to 1.1 × 10 − 21 and 4.5 × 10 − 19 . These results provide a practical basis for further improving the performance of transportable optical clocks.
We present the current status of the Sr+optical atomic ion clock at the National Research Council of Canada including the study of the quantum projection noise (QPN) limited stability and the progress on the evaluation of the blackbody radiation (BBR) shift uncertainty. The latest QPN limited stability of NRC's Sr+ clock is 3 × 10-15at 1 sec averaging time. The fractional evaluated accuracy of the Sr+ ion clock has reached 1.2 × 10-17and is now dominated by the BBR shift uncertainty, the improved evaluation of which is currently in progress.