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Chinese Physics Letters

Remote Comparison of Two Sr Optical Lattice Clocks through a 58 km Fiber Link

Tang-Yin 堂银 Liao 廖, Hao 豪 Liu 刘, Fei Meng, Qiang Wang, Tao Yang, Haochen Tian, Bing-Kun Lu, Lin Zhu, Ye Li, Baike Lin, Zhanjun Fang, Yige Lin

Published Feb 17, 2025• 3 citations

Abstract

Abstract Two 87Sr optical lattice clocks (OLCs) are being developed and operated at the National Institute of Metrology (NIM), located on different campuses that are 40 km apart. In order to compare the optical frequencies of these two Sr OLCs, a 58-km noise canceled fiber link is built to transfer both a 1542-nm transfer laser and a microwave reference from Changping campus to Hepingli campus. Two commercial optical frequency combs (OFCs) with adapted single-branch 698/1542 nm outputs coherently unite the two 698-nm clock lasers and the 1542-nm transfer laser. The fractional instability of the comparison yields 3.1 × 10−17 at 10000 s averaging time. The measured fractional frequency difference between these two Sr OLCs was evaluated to be 1.9(3.2) × 10−17, which is within their claimed uncertainties. This result demonstrates the consistency of their frequencies when they serve as optical frequency standards. Our remote comparison demonstrates the feasibility of optical clock comparison through a long-distance fiber link and contributes to the progress of redefinition of the SI second.

DOI: 10.1088/0256-307x/42/3/034201

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Abstract Two 87Sr optical lattice clocks (OLCs) are being developed and operated at the National Institute of Metrology (NIM), located on different campuses that are 40 km apart. In order to compare the optical frequencies of these two Sr OLCs, a 58-km noise canceled fiber link is built to transfer both a 1542-nm transfer laser and a microwave reference from Changping campus to Hepingli campus. Two commercial optical frequency combs (OFCs) with adapted single-branch 698/1542 nm outputs coherently unite the two 698-nm clock lasers and the 1542-nm transfer laser. The fractional instability of the comparison yields 3.1 × 10−17 at 10000 s averaging time. The measured fractional frequency difference between these two Sr OLCs was evaluated to be 1.9(3.2) × 10−17, which is within their claimed uncertainties. This result demonstrates the consistency of their frequencies when they serve as optical frequency standards. Our remote comparison demonstrates the feasibility of optical clock comparison through a long-distance fiber link and contributes to the progress of redefinition of the SI second.

We demonstrate a 30-km-long optical fiber link for frequency comparison between two strontium optical lattice clocks being developed at RIKEN and the University of Tokyo. We use a transfer laser at 1397 nm, which is twice the wavelength of the clock transition of strontium clocks. The link stability is estimated to be 1 × 10−17 for an averaging time of τ = 1 s, which is in good agreement with the theoretical limit calculated from the fiber noise spectrum. We discuss a remote clock comparison with a stability of 1 × 10−17(τ/s)−1/2 by synchronously operating two distant clocks.

Optical clocks and their associated frequency comparison networks are exceptionally sensitive to microscopic physical variations and thus capable of measuring fundamental physical quantities across diverse applications. In frequency comparison networks, the optical frequency combs (OFCs) act as accurate frequency sensors designed to translate terahertz optical signals down to radio frequency signals for accurate frequency counting. The number of OFC's comb modes that beat with clock and transfer lasers during remote frequency comparison is indispensable for the calculation of their frequency difference. In this work, with the assistance of a 1542 nm cavity-stabilized laser at Changping campus, the number of comb modes is locally determined with sufficient uncertainty by stepping the comb's repetition rate. This approach bypasses the technical challenges of simultaneous operation of optical clocks, OFC and fiber-link noise cancelation during long-distance comparison, providing a reliable prerequisite for remote optical clock comparisons.

Direct Comparison of Distant Optical Lattice Clocks at the

10^{-16}

Uncertainty

Fiber-based remote comparison of 87 Sr lattice clocks in 24 km distant laboratories is demonstrated. The instability of the comparison reaches 5 × 10 -16 over an averaging time of 1000 s, which is two orders of magnitude shorter than that of conventional satellite links and is limited by the instabilities of the optical clocks. By correcting the systematic shifts that are predominated by the differential gravitational redshift, the residual fractional difference is found to be (1.0±7.3) × 10 -16 , confirming the coincidence between the two clocks. The accurate and speedy comparison of distant optical clocks paves the way for a future optical redefinition of the second.

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10(-17) via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10(-17) is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

We demonstrate a 30-km-long optical fiber link for frequency comparison between two strontium optical lattice clocks being developed at Riken and the University of Tokyo. We use a transfer laser at 1397 nm which is twice the wavelength of the clock transition of strontium clocks. The link stability is estimated to be 1×1017for an averaging time τ = 1 s, which is in good agreement with the theoretical limit calculated from the fiber noise spectrum. We discuss a remote clock comparison with stability of 10 (τ/s) by synchronously operating the two distant clocks.

Atomic clock frequency ratios with fractional uncertainty

\leq 3.2 \times 10^{-18}

We report high-precision frequency ratio measurements between optical atomic clocks based on

^{27}

Al

^+

,

^{171}

Yb, and

^{87}

Sr. With total fractional uncertainties at or below

3.2 \times 10^{-18}

, these measurements meet an important milestone criterion for redefinition of the second in the International System of Units. Discrepancies in

^{87}

Sr ratios at approximately

1\times10^{-16}

and the Al

^+

/Yb ratio at

1.6\times10^{-17}

in fractional units compared to our previous measurements underscore the importance of repeated, high-precision comparisons by different laboratories. A key innovation in this work is the use of a common ultrastable reference delivered to all clocks via a 3.6 km phase-stabilized fiber link between two institutions. Derived from a cryogenic single-crystal silicon cavity, this reference improves comparison stability by a factor of 2 to 3 over previous systems, with an optical lattice clock ratio achieving a fractional instability of

1.3 \times 10^{-16}

at 1 second. By enabling faster comparisons, this stability will improve sensitivity to non-white noise processes and other underlying limits of state-of-the-art optical frequency standards.