A new approach transporting frequencies via commercially available fiber makes it possible to use optical atomic clocks to precisely measure height differences between locations thousands of kilometers apart, a development that could have implications for quantum mechanics, geodesy and radio astronomy.

The tick rate of a clock is influenced by gravity, so time runs slightly faster on clocks the farther they are from Earth’s surface – an effect called gravitational redshift. For a height difference of 1 m, the rate (frequency) of a clock changes by one part in 10¹⁶. The new method is sensitive enough to measure frequency deviations caused by height differences of just a few centimeters.

“But how can I measure the height difference – i.e., this frequency difference, – if the two clocks are not standing side by side?” said Gesine Grosche, a physicist at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig. “That is to say, how can I establish the connection to a second clock which is standing where a height must be measured with such accuracy?”

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The Earth represented as a geoid; i.e., when the actual distribution of the gravitational potential is shown. Here, the heights of the “bumps,” which are caused by the gravitational field of the Earth, have been determined by the Goce satellite. Although the data are precise as far as the respective height of the bumps, the lateral resolution amounts to a few kilometers. In the future, frequency comparisons between optical atomic clocks can be used to determine the height of the smaller structures and places on Earth. Courtesy of the European Space Agency.

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Researchers from Max Planck Institute of Quantum Optics (MPQ) in Garching and PTB used commercial optical fibers and a sophisticated amplifier technique to transport the frequency of one atomic clock to another over a distance of nearly 2000 km. The frequencies at both ends of the fiber link were compared using a highly sensitive interferometry method and found to be accurate to 19 digits.

The group first realized a frequency comparison over the 920 km between the MPQ and PTB last year, and has since doubled this range while achieving even better stabilities. Stefan Droste of MPQ said the total measurement uncertainty is just four parts in 10¹⁹, allowing a height difference of 4 mm between clocks to be resolved within 100 seconds of measurement time once the clocks support such accuracy.

This method could help geodesists in standardizing sea-level measurements, possibly surpassing the accuracy of GPS technologies, the researchers say. Because different countries use different points of reference in determining sea level, measurements worldwide are inconsistent. Geodesists potentially could re-compute sea level on the basis of the Earth’s gravitational force to determine the so-called geoid of the Earth to within a few centimeters.

Researchers from the MPQ and PTB as well as French researchers have also used this method of frequency transport via fiber to carry out spectroscopic investigations on hydrogen, which are important for understanding quantum mechanics. The work on optical-frequency transfer appeared in Physical Review Letters (doi: 10.1103/physrevlett.111.110801).