Lasers, seen here as red dots, have been used to create an optical lattice to trap an extremely cold gas of strontium atoms. The atoms are held in a vacuum and probed by a clock laser, yielding an exceptionally precise and accurate ticking rate. [Image: K. Palubicki/NIST]
Research groups around the world are racing to make the most stable and accurate optical clocks. A team at JILA and the University of Delaware, USA, has now edged ahead in that race by making painstaking measurements of tiny shifts in the frequency of tens of thousands of strontium atoms held in an optical lattice (Phys. Rev. Lett., doi: 10.48550/arXiv.2403.10664), achieving a systematic uncertainty of better than one part in a billion billion.
Optical versus microwave
Conventional atomic clocks pin the frequency of a microwave oscillator to a specific transition in cesium atoms by firing the microwaves at a group of atoms, varying the frequency across a narrow range and monitoring for a peak in fluorescence. The precision of this measurement can be improved by repeating the process many times so as to average away instability, which is the atoms' internal variation in ticking rate. But the higher the transition frequency, the quicker this can be done.
Optical clocks typically operate at frequencies about a million times higher than those of cesium clocks, thanks to their use of lasers as oscillators. This leads to far more precision and with it, much more accuracy―given that less time is needed to identify and potentially then remove sources of systematic error. While the best microwave clocks can reach stabilities and accuracies of around one part in 1016, optical timekeepers can get down to at least 10-18 on both fronts.
Indeed, many scientists are now looking to overhaul the SI second so that it is defined in terms of a specific optical, rather than microwave, transition. The superior performance of optical clocks could also lead, among other things, to better satellite navigation, geodesy and tests of general relativity―the latter thanks to improved measurements of gravitational redshift, which dictates that a clock ticks more slowly the closer it is to a massive body.
More precise ticking
Until now, the record for timekeeping accuracy was held by David Leibrandt (now at the University of California, Los Angeles, USA) and colleagues at the National Institute of Standards and Technology in Boulder, CO, USA. They made exquisite measurements of an optical transition in a single ion of aluminum―trapping it using an electric field and cooling it through a Coulomb interaction with a magnesium ion―achieving a systematic uncertainty of 9.4 × 10−19.
Indeed, many scientists are now looking to overhaul the SI second so that it is defined in terms of a specific optical, rather than microwave, transition.
Single ions have the advantage of being a very clean system, largely isolated from the effects of other particles. But because they are just a single timekeeper, it takes a long time to average away the fluctuations in ticking rate.
The latest work, like many others, instead uses thousands of neutral atoms held in a lattice by laser beams. Since instability decreases as the square root of both the number of measurements and the number of atoms, a given precision can be reached much more quickly in such a system.
Jun Ye and colleagues hold about 40,000 strontium-87 atoms in a vertical lattice containing thousands of layers―each one formed from a standing-wave laser beam―and then interrogate a very narrow optical transition using a laser stabilized to a resonator. Despite the atoms being maintained at just a few hundred nanokelvin, the vacuum chamber used to carry out the experiment is held at room temperature, which is more manageable.
Black-body-radiation shift
In 2022, the researchers reported having improved the stability of their clock by reducing the depth of the potential well in each lattice level, finding what they call a “magic lattice depth.” This allowed them to reduce the shift in clock laser frequency induced by both the lattice lasers and interactions between atoms, meaning in turn that they could use far more atoms than they had previously. Now, they have shown how to exploit that higher stability to raise the accuracy, making even more refined measurements of the various sources of systematic error that knock the ticking rate of the strontium atoms very slightly off kilter.
Most important of these is the copious black-body radiation in the experiment's environment. This induces a frequency shift that scales very quickly with temperature, calling for detailed knowledge of temperature variations. Placing two platinum resistance sensors in the middle of the vacuum chamber, the researchers observed roughly millikelvin temperature fluctuations at and below the hourly scale, as well as a similar-sized drift over the course of a day. They also measured the homogeneity of the vacuum chamber's temperature, ensuring a thermalized environment.
Now, they have shown how to exploit that higher stability to raise the accuracy, making even more refined measurements of the various sources of systematic error that knock the ticking rate of the strontium atoms very slightly off kilter.
The researchers also improved measurements of the relevant atomic radiation properties to account for higher-order corrections induced by black-body radiation in a realistic atom with discrete energy levels. Combining these measurements together, Ye and colleagues were able to reduce black-body uncertainty to 7.3 parts in 1019. Taken together with eight other sources of frequency shift, all smaller and most much smaller, they arrived at a total systematic uncertainty of 8.1 x 10-19.
This beats the NIST group by about 14%, but Ye says it should be possible to improve on that and get down to about 1 x 10-19 by housing the vacuum chamber in a cryogenic environment. He says that a number of groups are now working to this end, but that his own is currently concentrating on exploiting its already high precision. “We have a lot of exciting physics, including quantum metrology, many-body quantum physics and gravity, which we are exploring with our clock at the moment,” he says.