# Measuring height by connecting clocks

Especially interesting for
• geodesy
• fundamental research

How far above sea level is a place located? And where exactly is “sea level”? One of the objectives of the geodesists is to answer this question with 1 cm accuracy. Conventional measurement procedures or GPS technologies via satellites, however, have reached their limits here. Now, optical atomic clocks offer a new approach, because the tick rate of a clock is influenced by gravity. This wellknown, but tiny effect was measured by means of optical clocks a few years ago; these were, however, located at the same institute. Now, also up to 2,000 km may lie between them. This has been demonstrated by a cooperation between scientists of PTB and of the Max Planck Institute of Quantum Optics (MPQ) in Garching.

“Sea level”, in Germany, refers to the North Sea and differs by 27 cm from the sea level used in Switzerland, since the latter refers to the Mediterranean Sea. The different reference systems have already led to errors in large-scale bridge construction projects. Geodesists would therefore like to calculate a new uniform “sea level” which would be based on the gravitational force of the Earth. They want to determine the so-called “geoid” – a computational model of the Earth which exhibits the same gravitational potential everywhere – with such accuracy that it corresponds to a deviation of only a few centimetres. Hereby, they can rely on the support of the latest generation of optical atomic clocks. These can realize frequencies with such accuracy that even the smallest frequency deviations, which are caused by a height difference of a few centimetres, can be detected. What lies behind this is Einstein's general theory of relativity – concretely, the so-called “gravitational red shift”: If a clock is further way from the Earth, i.e. if it is in a weaker field of gravity, time actually runs a little faster for it. For a height difference of one metre, the rate (i.e. the frequency) of a clock changed by 1 ∙ 10–16.

Three years ago, it was demonstrated that a difference in height of 33 cm between two practically neighbouring clocks already has a measurable influence on their frequency. Within the scope of the present cooperation, optical precision frequencies were sent on a 1840 km trip in order to measure the difference in height of clocks that are located far away from each other. This was done using commercial glass-fibre networks and an ingenious amplification technique. Although the distance was twice the length of the previous experiment of the same kind, the stability was even further improved. The total measurement uncertainty was 4 ∙ 10–19. This would mean a height difference of 4 mm. And this resolution was attained after 100 seconds only.

In principle, optical clocks in research institutes which are further away can now be quasi-“interconnected” and used for all purposes for which such stable and well-defined frequencies are required. One of the first applications for basic research was spectroscopic investigations on hydrogen for the investigation of quantum-mechanical models. Geodetic issues will now be investigated in more depth in a special research field of PTB and Hannover University with Bremen University. This special research field has now been applied for.

### Contact

Gesine Grosche
Department 4.3 Quantum Optics and Unit of Length
Phone: +49 (0)531 592-4340
gesine.grosche(at)ptb.de

### Scientific publication

S. Droste, F. Ozimek, Th. Udem, K. Predehl, T. W. Hänsch, H. Schnatz, G. Grosche, R. Holzwarth: Optical frequency transfer over a single-span 1840 km fiber link. Phys. Rev. Lett. 111, 110801 (2013)