🔬 atomic physics

An \Al clock with $1.6\times10^{-18}$ systematic uncertainty and its frequency ratios

This paper reports the full systematic evaluation of an Al $^+$ single-ion optical clock achieving a fractional frequency uncertainty of $1.6\times10^{-18}$ , alongside precise measurements of its absolute frequency and its ratio to a Sr optical lattice clock, which show a significant deviation from previous BACON collaboration results and support the ongoing redefinition of the second.

Original authors: Fabian Dawel, Johannes Kramer, Derwell Drapier, Lennart Pelzer, Kai Dietze, Mirza A. Ali, Marek Hild, Vincent Barbé, Steven A. King, Joshua Klose, Kilian Stahl, Johannes Rahm, Navraj Poudel, Sören Dör

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Fabian Dawel, Johannes Kramer, Derwell Drapier, Lennart Pelzer, Kai Dietze, Mirza A. Ali, Marek Hild, Vincent Barbé, Steven A. King, Joshua Klose, Kilian Stahl, Johannes Rahm, Navraj Poudel, Sören Dörscher, Stefan Weyers, Erik Benkler, Christian Lisdat, Piet O. Schmidt

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine time as a river. For decades, we've measured the speed of that river using a very good, but slightly wobbly, stopwatch based on the vibrations of cesium atoms (the current definition of a "second"). Now, scientists have built a new kind of stopwatch using a single aluminum ion that is so precise it barely wobbles at all. This new clock is so accurate that if it had started ticking at the beginning of the universe, it would be off by less than a second today.

This paper is the "quality control report" for that new aluminum clock, built by a team at the Physikalisch-Technische Bundesanstalt (PTB) in Germany. Here is what they found, explained simply:

1. The Goal: Building a Better Stopwatch

The scientists wanted to prove that their aluminum clock is ready to replace the old cesium one. To do this, they had to do two things:

Check the internal mechanics: They had to find every tiny thing that could make the clock tick too fast or too slow (like a speck of dust on a gear) and calculate exactly how much it matters.
Compare it to other clocks: They compared their aluminum clock to two other top-tier clocks in the lab: a strontium lattice clock (made of many atoms) and the official cesium fountain clocks (the current gold standard).

2. The "Tuning" Process: Fighting Invisible Forces

The aluminum ion is trapped in a vacuum chamber, but it's not perfectly still. The team had to account for several "invisible forces" that try to mess up the timekeeping. Think of these as environmental noises:

Magnetic Fields: Just like a compass needle, the ion reacts to magnetic fields. The team used a specific trick (averaging two different states) to cancel out the main magnetic noise, leaving only a tiny, manageable whisper of uncertainty.
The "Jitter" of the Trap: The ion is held by radio waves. Sometimes, these waves push the ion slightly off-center, making it jitter. This is called "excess micromotion." The team used a second ion (calcium) as a "messenger" to feel this jitter and push the aluminum ion back to the center, like a dance partner correcting your steps.
Heat and Collisions: Even in a vacuum, stray gas molecules can bump into the ion, and heat from the walls can radiate energy. The team measured the temperature and the pressure of the vacuum chamber to calculate exactly how much these bumps and heat waves slowed the clock down.
The "Doppler" Effect: If the ion moves toward or away from the laser beam used to read the clock, the pitch changes (like a passing siren). The team shined lasers from opposite directions to cancel this effect out.

After accounting for all these factors, they calculated the clock's total "systematic uncertainty" to be 1.6 × 10⁻¹⁸.

The Analogy: This number is so small it's hard to grasp. Imagine measuring the distance from the Earth to the Sun. This clock is so precise that if you measured that distance, your error would be smaller than the width of a single human hair.

3. The Big Discovery: A Mystery Discrepancy

Here is where it gets interesting. The team compared their aluminum clock to a strontium clock (another ultra-precise clock made of strontium atoms) at the same lab.

The Result: They measured the ratio of the two clocks' frequencies (how many times the aluminum clock ticks for every strontium tick).
The Surprise: Their result did not match a previous measurement made by a famous international group called "BACON" (Boulder Atomic Clock Optical Network).
- Compared to the BACON result from 2021, their result was off by 8.6 standard deviations. In science, this is a massive difference, like flipping a coin 10 times and getting heads every single time when you expected a mix.
- Compared to a newer BACON result from 2025, it was still off, but only by 1.2 standard deviations.

What this means: The paper doesn't say one clock is "wrong" and the other is "right." Instead, it highlights that when different labs measure these incredibly precise clocks, they sometimes get slightly different answers. This suggests that there are still tiny, hidden factors we don't fully understand yet. It's a call for more independent teams to check their work to solve the mystery.

4. The Absolute Time

The team also measured the "absolute frequency" of their aluminum clock—essentially, how many times it ticks in one second. They found it ticks 1,121,015,393,207,859.19 times per second. This number matches what other top labs (like NIST in the US) have found, giving confidence that the clock is working correctly.

Summary

This paper is a rigorous "health check" for a super-precise aluminum ion clock.

It works: The clock is incredibly stable and accurate, with a systematic uncertainty of 1.6 × 10⁻¹⁸.
It's ready: It is a strong candidate to help redefine the international "second" in the future.
The Puzzle: There is a significant disagreement between this lab's measurement of the aluminum-to-strontium clock ratio and a previous measurement by the BACON collaboration. This discrepancy proves that even at this level of precision, we need more independent checks to ensure we truly understand how these clocks behave.

The paper concludes that while we have made huge progress, the fact that different labs see slightly different results at this level of precision is a reminder that science is an ongoing process of checking and re-checking.

Technical Summary: Evaluation of an Al $^+$ Clock with $1.6 \times 10^{-18}$ Systematic Uncertainty and Frequency Ratios

Problem and Motivation
Optical clocks based on trapped ions and neutral atoms have surpassed microwave clocks in stability and accuracy by more than two orders of magnitude, reaching systematic uncertainties in the low $10^{-18}$ range. These advancements motivate a redefinition of the SI second, a process that requires rigorous evaluation of systematic uncertainties and robust consistency among different clock realizations. While frequency ratio measurements between clocks of the same species have been performed, discrepancies at the $10^{-17}$ level have been identified between different species and institutions. This underscores the necessity for independent validation of optical clocks, particularly for candidate systems like the aluminum ion ( $^{27}\text{Al}^+$ ), to ensure the reliability required for a future redefinition of the second.

Methodology
The authors present a full evaluation of a single-ion $^{27}\text{Al}^+$ clock at the Physikalisch-Technische Bundesanstalt (PTB) in Germany. The clock utilizes quantum logic spectroscopy with a co-trapped $^{40}\text{Ca}^+$ ion for state preparation, cooling, and readout.

Experimental Setup: A linear Paul trap confines an $^{27}\text{Al}^+$ / $^{40}\text{Ca}^+$ ion crystal. The system operates in an ultra-high-vacuum chamber ( $11(6)$ nPa). A magnetic bias field of 0.15 mT is stabilized to $<2$ nT.
Clock Operation: The clock interrogates the $^1\text{S}_0 \leftrightarrow {}^3\text{P}_0$ transition of $^{27}\text{Al}^+$ . The cycle involves optical pumping, Doppler cooling of the $^{40}\text{Ca}^+$ ion, and Electromagnetically Induced Transparency (EIT) cooling to prepare the motional ground state. The clock transition is probed using a Ramsey sequence with 25 ms $\pi/2$ pulses and a 250 ms dark time. Continuous EIT cooling is applied during interrogation to minimize the time dilation shift (TDS).
Systematic Shift Evaluation: The authors evaluated all relevant systematic frequency shifts, including:
- Magnetic Fields: First-order Zeeman shifts are suppressed by averaging $\Delta m_F = 0$ transitions. Second-order shifts are calculated using measured field strengths and atomic coefficients.
- Doppler Effects: First-order Doppler shifts are determined by comparing counter-propagating probe beams. Time dilation shifts (TDS) are calculated based on sideband thermometry of the motional modes.
- Excess Micromotion (EMM): EMM is monitored and compensated using phase-modulated sideband spectroscopy (PMSS) on the $^{40}\text{Ca}^+$ ion, with shifts transferred to $^{27}\text{Al}^+$ .
- Light Shifts: AC Stark shifts from the clock laser, cooling lasers, and EIT cooling lasers are evaluated, with the latter being a dominant uncertainty source due to differential polarizability.
- Collisions: Shifts due to background gas collisions are modeled based on pressure measurements and theoretical models.
- Other Effects: Servo errors, blackbody radiation (BBR) shifts, and electric quadrupole shifts are quantified.

Key Contributions and Results

Systematic Uncertainty Budget: The total systematic fractional frequency uncertainty of the $^{27}\text{Al}^+$ clock is evaluated to be $1.6 \times 10^{-18}$ . The primary limitations are the accuracy of relevant atomic coefficients (specifically for AC Stark shifts and magnetic g-factors) and background gas collisions.
Absolute Frequency Measurement: The absolute frequency of the $^{27}\text{Al}^+$ clock was measured via comparison with PTB's primary caesium fountain clocks (CSF1 and CSF2) and the $^{87}\text{Sr}$ optical lattice clock. The result is:
$\nu_{\text{Al}^+} = 1\,121\,015\,393\,207\,859.19(24) \text{ Hz}$
This corresponds to a relative uncertainty of $2.1 \times 10^{-16}$ .
Frequency Ratio Measurement: The frequency ratio between the $^{27}\text{Al}^+$ clock and the PTB $^{87}\text{Sr}$ optical lattice clock (Sr3) was determined to be:
$\nu_{\text{Al}^+}/\nu_{^{87}\text{Sr}} = 2.611\,701\,431\,781\,462\,668(36)$
This measurement is limited by the accuracy of the Sr clock ( $1.3 \times 10^{-17}$ ).

Discrepancies and Validation
The measured frequency ratio differs by $8.6\sigma$ from the 2021 value published by the BACON collaboration and by $1.2\sigma$ from their 2025 value. The authors note that this discrepancy highlights the critical need for independent measurements of clock-candidate frequency ratios across different institutions to validate estimated systematic uncertainty budgets.

Significance
The paper claims that these results represent an important contribution toward the future redefinition of the second using optical clocks. By demonstrating a systematic uncertainty of $1.6 \times 10^{-18}$ and providing an independent frequency ratio measurement, the work supports the inclusion of $^{27}\text{Al}^+$ as a candidate system. However, the observed deviations at the $10^{-17}$ level between institutions serve as a reminder that inter-institutional comparisons remain essential for the validation of optical clocks before a redefinition can be finalized.

1. The Goal: Building a Better Stopwatch

2. The "Tuning" Process: Fighting Invisible Forces

3. The Big Discovery: A Mystery Discrepancy

4. The Absolute Time

Summary

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