Absolute frequency measurement of the $^{40}$Ca$^{+}$ clock transition using a GNSS link to the SI second

Time, in the most fundamental sense, is measured by counting the steady, rhythmic ticks of an atom. For decades, the world's official seconds have been defined by the vibrations of cesium atoms, a standard that has served humanity well. However, scientists have long sought a more precise way to keep time, one that relies on atoms vibrating at much higher speeds, using light instead of microwaves. These optical atomic clocks are so sensitive that they can detect the tiniest changes in gravity or the passage of time itself. To be useful, these clocks must be compared against the official time kept by national laboratories, but doing so requires a bridge that can carry the signal across hundreds of kilometers without losing its precision.

In a recent study, researchers in Innsbruck, Austria, built such a bridge to measure the exact frequency of a specific clock based on a single calcium ion. They connected their laboratory to the primary timekeeping center in Braunschweig, Germany, using a network of navigation satellites. By doing this, they determined the absolute frequency of the calcium clock transition with a level of precision that had never been achieved before for this specific setup. Their work not only provides a new, highly accurate number for how fast this clock ticks but also corrects a long-standing discrepancy in the scientific record and refines our understanding of how magnetic fields interact with the atom.

The experiment centered on a single calcium ion, an atom that has lost one electron, trapped in a vacuum chamber by invisible electric and magnetic forces. This ion acts as the pendulum of the clock. To make it tick, the researchers shine a laser beam of a very specific color, deep red, onto the atom. When the laser's frequency matches the natural vibration of the ion, the atom absorbs the energy and jumps to a higher energy state. The researchers are looking for the exact moment this happens, which occurs at a frequency of 411,042,129,776,401.2 hertz. This number represents the number of times the atom vibrates every second. To measure this with such extreme accuracy, they had to ensure that no external factor, such as stray magnetic fields or the heat of the surrounding environment, was pushing the number slightly off.

To connect their local clock to the international standard, the team established a link to the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, the German national metrology institute that helps define Coordinated Universal Time. They used a passive hydrogen maser, a device that generates a very stable signal, as a local reference. This signal was then compared to the time kept by satellites in the Global Navigation Satellite System. By analyzing the time it took for signals to travel between their lab, the satellites, and the German laboratory, they could calculate the precise difference between their local clock and the official international time. This method, known as Precise Point Positioning, allowed them to transfer the time standard over a distance of several hundred kilometers with minimal error.

The measurement campaign lasted ten days in June 2021. During this time, the researchers probed the ion six different times, using slightly different magnetic settings for each probe. This clever strategy allowed them to cancel out several sources of error that usually plague such measurements, including shifts caused by the Earth's magnetic field and the electric fields inside the trap. However, they discovered that a subtle effect caused by the radio-frequency currents used to hold the ion in place was still influencing the results. These currents create a tiny, oscillating magnetic field that shifts the energy levels of the atom in a way that had not been fully accounted for in previous measurements. By carefully measuring this effect, the team was able to correct their data and also calculate a new, more accurate value for a fundamental property of the calcium atom known as the Landé g-factor, which describes how the atom responds to magnetic fields.

The final result of their work is a measurement of the calcium clock transition frequency with a fractional uncertainty of 1.5 times 10 to the power of minus 15. To put this level of precision into perspective, if this clock had started ticking at the beginning of the universe, it would be off by less than a second today. This result places their measurement in agreement with the most recent studies from other laboratories in China and Israel, but it contradicts earlier measurements from 2009 to 2012. The researchers believe the earlier results were less accurate because they did not fully account for the oscillating magnetic fields generated by the trap itself. By including this factor, the new measurement resolves the disagreement and provides a more reliable standard for future timekeeping.

Beyond the specific number, the study demonstrates the power of using satellite links to compare the world's most advanced clocks. While fiber-optic cables can offer even better stability, they are not always practical to lay between distant cities. The satellite link used here offers a simpler, more accessible way to verify that optical clocks around the world are consistent with one another. The researchers also confirmed that their own measurements were limited primarily by the stability of their local hydrogen maser, suggesting that future improvements could be made by using an even more stable reference source. This work marks a significant step forward in the global effort to redefine the second and to use these incredibly precise clocks to test the fundamental laws of physics.