Making some of the most precise measurements ever, a network of researchers closely compared three clocks that track the activity of atoms to tell time, an important step toward formally redefining the second to a more accurate standard.

The frequency ratios between aluminum-ion, strontium and ytterbium atomic clocks were the first to be measured with an accuracy of 18 digits, with an uncertainty about one-third the size of the previous best. They were also applied to help guide scientists' search for the unknown identity of dark matter, an example of atomic clocks' potential in fundamental physics research in addition to keeping time.

Led by scientists from the University of Colorado Boulder and the National Institute of Standards and Technology, the group of scientific collaborators published their paper March 24 in Nature.

The second was once defined as 1/86,400 of a day on Earth, but scientists have since found more accurate ways to clarify the second's exact length than by referring to the planet's rotation. Since the 1967-68 meeting of the International Bureau of Weights and Measures, a second has been defined as the time it takes for a cesium-133 atom to oscillate between particular energy levels 9,192,631,770 times.

Atomic clocks measure these kinds of oscillations in cesium or other elements with extraordinary precision, and the measurements they produce are important to scientific research as well as technologies such as GPS. The official timekeeping clock of the U.S. is the NIST-F1, which was developed by the National Institute of Standards and Technology and has such a high level of precision that it would take more than 100 million years for it to gain or lose a second.

But scientists have been pushing time-measuring accuracy even further by developing optical atomic clocks, which track atomic oscillations that occur about 100,000 times more quickly. This grants optical atomic clocks higher fidelity in measuring time, said study author Colin Kennedy, a postdoctoral researcher at UC Boulder-affiliated physics research institute JILA.

"You can kind of think of it like a comb, in that an optical clock just has much finer teeth for you to get much finer resolution of time than the standard microwave definitions that we have right now," Kennedy said. "That's why optical clocks are important."

In a multiyear collaboration, several research groups connected JILA's strontium clock on the UC Boulder campus to the aluminum-ion and ytterbium clocks just under a mile away at NIST, using a fiber-optic line and a second wireless connection. Each clock generated a laser at the frequency being measured in their respective atoms, and the frequencies were compared with each other to generate three ratios.

"At the heart of all of these clocks is something that's very much the same thing, which is an extremely stable oscillator — that's what the atom serves as," said David Hume, a physicist at NIST and another author of the paper. "In the case of optical clocks, it's the electron in the atom that is oscillating at a million billion times a second or so."

The frequency-comparison ratios boasted uncertainties between six and eight parts per quintillion, a number represented by a one followed by 18 zeros. An equally precise measure of the Earth's 7,926-mile diameter at the equator would have an uncertainty of about 4 billionths of an inch, or around the size of a small atom.

The ratios are the three most precise measurements ever made, according to Kennedy, barring measurements of the value 1 to numerous decimal digits. He said these ratios are useful for reproducing and confirming the results of optical atomic clocks, whose direct measurements are challenging to transmit because of their high energy.

They are also an important step toward redefining the second. The International Bureau of Weights and Measures, the intergovernmental organization that oversees the metric system, laid out five milestones to be met before the second is formally redefined using optical atomic clocks. NIST's ytterbium clock met the first milestone in 2018 by being 100 times more accurate than the best cesium clock, and the most recent research makes progress toward the milestone related to comparing optical atomic clocks.

The measurements of the frequency-comparison ratios were so sensitive that the scientists needed to account for the usually negligible effects of general relativity on the atomic clocks, which they did by surveying the area to know the altitudes of their equipment.

Hume said, "General relativity tells us that time moves slower in a deeper gravitational potential, so if you take two clocks that are perfectly identical in every way and you move one up a few centimeters, then it will be ticking faster by a very, very small amount — a few parts in a billion billion."

The atomic-clock researchers also harnessed the unprecedented precision to narrow the search for dark matter, an unidentified form of matter that nevertheless imposes significant gravitational effects on the cosmological scale. The frequency-ratio measurements were used to put the tightest-yet constraints on the possible masses dark matter can be — specifically on ultralight dark matter, one theoretical form of it that would be incredibly small and low-energy.

The dark-matter application is one example of how atomic clocks can be used as a tool in physics research, which also includes testing whether fundamental constants really are constant and measuring differences in Earth's shape and gravity in different parts of the world.

The study used data that was collected between 2017 and 2018, and Hume said he looks forward to using the additional research that has been conducted since then to make even more precise measurements. Kennedy wants to see their work reproduced by other groups, which would generate greater confidence in the results and speed up the redefining process for the second.

"Reproducibility of these ratios is really the key aspect standing in the way between actually redefining the second in terms of an optical standard," Kennedy said. "We really need to see the same number measured by different labs using different approaches all over the world."

The study, "Frequency ratio measurements at 18-digit accuracy using an optical clock network," published March 23 in Nature, was authored by Kyle Beloy, Martha Bodine, Samuel Brewer, Jwo-Sy Chen, Scott Diddams, Robert Fasano, Tara Fortier, Youssef Hassan, David Hume, Isaac Khader, Amanda Koepke, David Leibrandt, Holly Leopardi, Andrew Ludlow, William McGrew, Nathan Newbury, Daniele Nicolodi, Thomas Parker, Stefania Romisch, Stefan Schäffer, Jeffrey Sherman, Laura Sinclair, William Swann, Jian Yao and Xiaogang Zhang, National Institute of Standards and Technology; Jean-Daniel Deschênes, Consultation OctoSig; Tobias Bothwell, Sarah Bromley, Dhruv Kedar, William Milner, John Robinson and Lindsay Sonderhouse, University of Colorado; and Colin Kennedy, Eric Oelker and Jun Ye, National Institute of Standards and Technology and University of Colorado.