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Applied Physics Letters

Synchronous frequency comparison beyond the Dick limit based on dual-excitation spectrum in an optical lattice clock

Xiaotong Lu, Chihua Zhou, Ting Li, Yebing Wang, Hong Chang

Published Dec 7, 2020• 8 citations
Publisher

Abstract

We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.

DOI
10.1063/5.0025097

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•May 1, 2026•0 citations
We present a synchronous frequency comparison method based on one cold-atom ensemble by using the dual-excitation spectrum technique, which can simultaneously detect the probabilities of two different clock transitions. We experimentally verify this synchronous frequency comparison method between |mF|=9/2 and |mF|=7/2 in a one-dimensional 87Sr optical lattice clock and the comparison instability is well below the Dick limit. We also extend the dual-excitation spectrum method to shorten the clock feedback cycle by a half in optical lattice clocks and experimentally demonstrate that the interleaved self-comparison instability is 1.4 times lower than that of the traditional operation method.
In this paper, we demonstrate in situ synchronous frequency comparison between distinct regions in a one-dimensional optical lattice. The synchronous comparison instability is well below the Dick limit and agrees with the limit induced by atomic detection noise. The absolute atom number is extracted from the synchronous comparison instability with an uncertainty below 3%. Surpassing the performance of absorption imaging, this method provides a way to directly and precisely determine the absolute atom number from detection noise. Taking advantage of the inhomogeneous density distribution over the whole lattice, the density shift can also be conveniently measured by this synchronous frequency comparison method. Inconsistent with the expectation of the linear relationship between density shift and atom number difference, nonlinearity is observed, indicating that the assumption of an identical density shift coefficient over the whole lattice is not always safe.
We demonstrate the frequency comparison of two optical lattice clocks at the relative stabilities close to the quantum projection noise (QPN) limit of optical lattice clocks. This stable frequency comparison is accomplished by synchronous interrogations of two clocks by a common probe laser, which allows us to cancel out the probe laser's frequency noise. We perform the frequency comparison of a one-dimensional (1D) optical lattice clock with spin-polarized fermions 87Sr and a three-dimensional (3D) optical lattice clock with unity-occupation bosons 88Sr and achieve the Allan standard deviation of σγ(τ)=4×10-16 τ-1/2, which corresponds to the QPN limited stability for N=1,000 atoms and the spectrum linewidth γ=8 Hz. The relative stability reaches 1×10-17 with an averaging time of 1,600 s. Finally, we discuss the prospects to realize 10-18 fractional inaccuracies and the possible application of frequency comparison with synchronous interrogations to remote clocks' comparison for relativistic geodesy.
Abstract Optical clocks are the most precise measurement devices. Here we experimentally characterize one such clock based on the 1S0-3P0 transition of neutral 171Yb atoms confined in an optical lattice. Given that the systematic evaluation using an interleaved stabilization scheme is unable to avoid noise from the clock laser, synchronous comparisons against a second 171Yb lattice system were implemented to accelerate the evaluation. The fractional instability of one clock falls below 4 × 10−17 after an averaging over a time of 5,000 seconds. The systematic frequency shifts were corrected with a total uncertainty of 1.7 × 10−16. The lattice polarizability shift currently contributes the largest source. This work paves the way to measuring the absolute clock transition frequency relative to the primary Cs standard or against the International System of Units (SI) second.
The experimental comparison of two thulium optical lattice clocks in a time interval of up to one hour has been carried out. The synchronous comparison of a clock transition in two independent atomic ensembles using a single ultrastable laser has allowed us to eliminate fluctuations of the laser frequency from the measured frequency difference and to reach a relative measurement error of 10–16 after 500-s averaging, which corresponds to a relative instability of 2×10−15/τ2 \times {{10}^{{ - 15}}}{\text{/}}\sqrt \tau 2×10−15/τ​ . The successful demonstration of the long-term operation of two systems using the synchronous comparison of clock transitions opens the possibility of studying systematic shifts in thulium optical clocks with an uncertainty of 10–17.
Optical atomic clocks have spurred a range of precision frequency comparison experiments and proposals including tests of general relativity, gravitational wave detection, and relativistic geodesy. Current measurements using optical atomic clocks are often limited by the coherence of the clock laser rather than the atomic samples used as a frequency reference. In order to overcome the performance limits imposed by clock laser coherence, we realize a multiplexed optical clock system where multiple spatially resolved ensembles each consisting of thousands of strontium atoms trapped in a 1D optical lattice function as separate atomic frequency references that can be simultaneously interrogated with a shared clock laser. This scheme allows us to make differential frequency comparisons with a quantum projection noise limited fractional instability of 9.7(4)×10−18/ √τ and a differential fractional uncertainty of 8.9×10−20 after 3.3 hours of averaging. We then use this system to perform a lab-based test of the gravitational redshift at the centimeter scale, where we measure a fractional frequency gradient of [−12.4±0.7stat ±2.5sys]×10−19/cm, consistent with the predicted value of 10.9×10−19/cm. Having demonstrated that our differential comparisons are no longer limited by the local oscillator, we turn to fundamental limits on atom–atom coherence. We perform a direct decay measurement of the natural lifetime of the excited clock state 3P0 in 87Sr, in which we use measurements of simultaneously loaded high and low density atomic ensembles and compare decay rates of 87Sr and 88Sr to help isolate natural lifetime decay from other population dynamics. We measure a lifetime of 167+79 −40, which is consistent with previously reported experimental and theoretical values. Lastly, we demonstrate a hyperfine-resolved readout scheme in 87Sr that converts depolarization errors during interrogation into erasure errors, extending coherence times between ensembles in our optical lattice clock up to 150s using spin-echo measurements. These results taken together demonstrate the advantages of differential clock measurements that aren’t limited by clock laser coherence and how to characterize and improve on the performance limits that arise in that regime.