Measuring the weakest of forces

Cold atoms detect a 174-yoctonewton force

A blob of cold beryllium ions has measured the smallest force yet. The charged atoms registered the minuscule tug of an electric field to be 174 yoctonewtons. That’s about equal to the force of Earth’s gravity on a 70-kilogram human divided by a million, then by a billion, then by a billion again, then by four.

“The forces measured are astonishingly small,” comments quantum physicist Dick Slusher of the Georgia Tech Quantum Institute in Atlanta. Slusher, who was not affiliated with the study, calls the research “wonderful work.”

The measurement technique, developed by researchers at the National Institute of Standards and Technology in Boulder, Colo., may lead to more precise ways of analyzing the fine-grained surface properties of materials.

The NIST scientists first trapped about 60 beryllium ions with electric and magnetic fields. These atoms were then cooled to about half a millikelvin with lasers. At such cold temperatures, the ions are very sensitive to the slightest perturbations and form the cores of “exquisitely sensitive force detectors,” the researchers led by Michael Biercuk, now at the University of Sydney, report in a manuscript published online at

Next, they hit the vulnerable ions with a force, delivered in the form of an electric field. The electric field bumped into the ions, changing their motion. This motion was detected with a technique that relied on lasers, called Doppler velocimetry. Light reflecting off the ions changed wavelength as the ions moved. (Cops use the same principle to determine car speeds with radar guns.) This telltale light change allowed the researchers to make the 174-yoctonewton measurement.

Adopted in 1991 as the smallest prefix in the International System of Units, known as the SI system, “yocto” means one part in a million billion billion, or 10-24.

Derived from the base “octo” (for the 8th power of 103), yocto got its “y” to prevent its abbreviation from being o, and thus confusable with the number zero. Yocto, and its gargantuan partner yotta, for 1024, are currently the smallest and largest recognized SI unit prefixes, although a group led by University of California, Davis students are pushing for formal recognition of the “hella” prefix to mean 1027.

The new method is the most explicit measurement of such a tiny force, says atomic physicist Dietrich Leibfried, also of NIST in Boulder, Colo. But in his opinion the achievement is diminutive in more ways than one, because many researchers are no strangers to such small forces. But until now, “people never really cared to write down how small such forces are,” he says. In a Nature Physics paper published last year, Leibfried and his colleagues estimated that their single-ion trap could detect forces as small as half a yoctonewton.  

The method presented in the new paper is bound to have valuable applications in the future, Slusher says. One possible use would be to measure minuscule changes in the electric field near metal surfaces. “The origin of these tiny field fluctuations is still a mystery,” and this very sensitive measurement system might be a valuable tool for understanding such fluctuations and how to counter them.

Laura Sanders is the neuroscience writer. She holds a Ph.D. in molecular biology from the University of Southern California.

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