International Optical Clock Comparison Using the European Optical Fiber Network

This paper reports a successful two-month international comparison of seven optical clocks across four European metrology institutes via a fiber network, achieving frequency ratio uncertainties as low as $7.7\times10^{-18}$ and providing critical data for the future redefinition of the SI second.

The Gist

Imagine you have the world's most perfect watches. These aren't your standard wristwatches; they are optical clocks that tick so precisely they would only lose or gain a single second over the entire age of the universe. Scientists have built these incredible timekeepers in different countries, but for a long time, they couldn't be sure if the watch in Italy was ticking at the exact same speed as the one in Germany or the UK.

This paper is like a report card on a massive, two-month-long "timekeeping Olympics" held in early 2023. Here is what happened, explained simply:

The Setup: A High-Speed Time-Traveling Network

Usually, to compare two watches in different countries, scientists use satellites (like GPS). But satellites are a bit like trying to compare two watches by shouting across a windy canyon; the signal gets a little fuzzy, and the comparison isn't perfect.

Instead, these scientists used a giant, super-stable fiber-optic cable network stretching across Europe. Think of this network as a "super-highway" for light. They connected four major metrology labs (in Italy, France, Germany, and the UK) with these cables. This allowed them to send the "tick" of one clock directly to another without the fuzziness of satellites.

The Contestants: Seven Different Clocks

Seven different clocks entered the race. They weren't all made the same way:

• Some used Ytterbium (a metal) trapped as a single ion (like a tiny, floating marble).
• Some used Strontium or Mercury atoms trapped in a "lattice" (like a honeycomb made of light).
• They operated on different types of "transitions" (ways the atoms jump energy levels), which is like different clock brands using different internal gears.

The Big Achievement: The "Twin" Check

The most exciting result came from comparing two clocks that were built independently in two different countries (one in the UK, one in Germany). Both were Ytterbium ion clocks using a specific, very complex type of tick (called the "E3" transition).

• The Result: They agreed with each other perfectly, within a tiny margin of error (less than 1 part in 100 quadrillion).
• The Analogy: Imagine two master watchmakers in different cities build a clock from scratch. They send their clocks to a neutral ground. When they compare them, the hands are in the exact same position, down to a fraction of a hair's width. This was the first time two independently built optical clocks from different countries were proven to agree at this level of precision.

The Mercury Clock: A New Champion

The clock in France, which uses Mercury, was also a star player. It was compared against all the other clocks in the network. The results showed that the Mercury clock is incredibly stable and reliable, providing new, highly precise measurements of how its "tick" compares to the Ytterbium and Strontium clocks.

Why This Matters (According to the Paper)

The paper explains that the world is currently trying to redefine the "second." Right now, the second is defined by microwave clocks (the old standard). Scientists want to switch to these new, super-precise optical clocks.

However, before you can change the definition of a second, you have to prove that every optical clock in the world agrees on what a second is. If the clock in Paris says "one second" is slightly different than the clock in London, you can't change the rule.

This experiment proved that:

1. The Network Works: The fiber-optic cables are so good that they don't mess up the comparison. They are essentially invisible to the measurement.
2. The Clocks Agree: Different types of optical clocks, built by different teams in different countries, are all telling the same time with incredible accuracy.

The "Glitch" in the System

The paper also mentions one clock (a Strontium clock in Germany) that had a "sickness." It was affected by a laser issue that shifted its time slightly. The scientists couldn't fix this after the fact, so they didn't include its final numbers in the main results. However, they still used it to check how stable the other clocks were, because even with its sickness, it was very steady in the short term.

The Bottom Line

This paper is a victory lap for international science. It shows that we have built a "web of time" across Europe that is so precise we can finally trust that our best clocks are all synchronized. This is a crucial step toward updating the official definition of time itself, ensuring that the "second" we use tomorrow is as perfect as the clocks we built today.

Technical Summary

1. Problem Statement

Optical clocks have achieved fractional frequency uncertainties at the $10^{-18}$ level and below, making them superior to current microwave-based SI second definitions. However, a critical bottleneck remains: verifying the international consistency of these clocks.

• The Challenge: While intra-laboratory comparisons are routine, comparing independent optical clocks across different countries is difficult. It requires reliable long-distance fiber links, synchronized operation of multiple complex systems, and the coordination of systematic uncertainty budgets.
• The Goal: To validate the redefinition of the SI second based on optical transitions, the scientific community must demonstrate that independently developed optical clocks (using different atomic species and technologies) agree with each other at the $10^{-18}$ level across international borders.

2. Methodology

The authors conducted a two-month international clock comparison campaign (February 24 – May 1, 2023) involving four National Metrology Institutes (NMIs) in Europe:

• Institutes: INRIM (Italy), LNE-OP (formerly LNE-SYRTE, France), NPL (UK), and PTB (Germany).
• Infrastructure: The comparison utilized the European phase-stabilized optical fiber network (REFIMEVE), connecting:
  • LNE-OP to NPL (785 km)
  • LNE-OP to PTB (1370 km)
  • LNE-OP to INRIM (1023 km)
• Clocks Involved (7 Total):
  • France (LNE-OP): $^{199}\text{Hg}$ optical lattice clock (SYRTE-Hg).
  • UK (NPL): $^{171}\text{Yb}^+$ ion clock (E3 transition) and $^{87}\text{Sr}$ optical lattice clock.
  • Germany (PTB): Two $^{171}\text{Yb}^+$ ion clocks (E3 and E2 transitions) and one $^{87}\text{Sr}$ optical lattice clock.
  • Italy (INRIM): $^{171}\text{Yb}$ optical lattice clock.
• Data Analysis:
  • Frequency ratios were calculated by comparing the optical frequencies of the clocks via the fiber links.
  • Statistical uncertainties were evaluated using daily bins and inflated by the Birge ratio if daily scatter exceeded expectations (indicating excess noise).
  • Systematic uncertainties included contributions from each clock's physics package, statistical noise, and relativistic redshift corrections.
  • Correlation coefficients were calculated for all measurement pairs to account for shared systematic errors (e.g., common reference clocks).

3. Key Contributions

• First Sub-$10^{-17}$ International Verification: The campaign achieved the first international comparison of two independently developed optical clocks ($^{171}\text{Yb}^+$ E3) with an uncertainty below $1 \times 10^{-17}$.
• Large-Scale Network Integration: Successfully coordinated the simultaneous operation of 7 distinct optical clocks across 4 countries over 65 days, demonstrating the maturity of the European fiber network for metrology.
• New Frequency Ratios: Provided the first direct international measurements of frequency ratios involving the $^{199}\text{Hg}$ clock against $^{171}\text{Yb}^+$ and $^{87}\text{Sr}$ clocks.
• Data Transparency: Released a comprehensive dataset including 11 frequency ratios, correlation matrices, and instability data, serving as a benchmark for future SI redefinition efforts.

4. Key Results

• $^{171}\text{Yb}^+$ (E3) Agreement (NPL vs. PTB):
  • The two $^{171}\text{Yb}^+$ clocks operating on the electric octupole (E3) transition agreed within an uncertainty of $7.7 \times 10^{-18}$.
  • This is a significant improvement over the previous GNSS-based comparison (ROCIT 2022), which had an uncertainty of $2.8 \times 10^{-16}$.
  • This result confirms the consistency of independently built ion clocks at the $10^{-18}$ level.
• $^{199}\text{Hg}$ Clock Performance:
  • The LNE-OP $^{199}\text{Hg}$ clock was compared against $^{171}\text{Yb}^+$ (E3), $^{171}\text{Yb}$, and $^{87}\text{Sr}$ clocks.
  • Results showed agreement with reference values (derived from a 2021 least-squares adjustment) at the $10^{-17}$ level.
  • The campaign provided new, lower-uncertainty direct measurements for the $^{199}\text{Hg}/^{171}\text{Yb}^+$ and $^{199}\text{Hg}/^{87}\text{Sr}$ ratios.
• $^{171}\text{Yb}$ Lattice Clock Consistency:
  • The INRIM $^{171}\text{Yb}$ lattice clock agreed with the PTB $^{171}\text{Yb}^+$ (E3) clock within $2.2 \times 10^{-17}$, confirming reproducibility with the 2022 ROCIT campaign.
• Anomalies and Inconsistencies:
  • PTB-Sr3: This clock exhibited a frequency shift (likely due to the clock laser) that could not be corrected retrospectively. Consequently, its absolute frequency ratios were not reported, though its instability data was used to assess the network's short-term performance.
  • $^{171}\text{Yb}/^{87}\text{Sr}$ Discrepancy: A $4\sigma$ discrepancy was observed between the INRIM/NPL $^{171}\text{Yb}/^{87}\text{Sr}$ ratio and earlier measurements by the BACON collaboration (NIST/JILA), though it aligns with RIKEN and newer BACON data. This highlights ongoing challenges in the consistency of different atomic species ratios.

5. Significance

• Path to SI Redefinition: These results are a crucial step toward the redefinition of the SI second. They demonstrate that the international metrology community can reliably compare optical clocks across borders with uncertainties approaching $10^{-18}$, a prerequisite for adopting an optical transition as the new time standard.
• Fiber Network Maturity: The study proves that the European optical fiber network is a robust, high-uptime infrastructure capable of supporting complex, multi-node metrology campaigns with negligible link-induced uncertainty.
• Beyond Metrology: The technology demonstrated here supports broader scientific applications, including:
  • Geodesy: Chronometric leveling for measuring geopotential differences.
  • Fundamental Physics: Testing General Relativity, searching for dark matter, and detecting variations in fundamental constants.
  • Quantum Communication: Enabling long-distance quantum key distribution and frequency distribution to radio telescopes.

In conclusion, this paper represents a landmark achievement in global metrology, validating the feasibility of a future "optical second" by proving that independent optical clocks can be compared internationally with unprecedented precision.