Field optical clocks and sensitivity to mass anomalies for geoscience applications

350 years ago, the pendulum clock for astronomical observations was diverted to become an instrument for measuring gravity. The measurement of the parallax of Mars by Richer and Cassini from Cayenne and Paris showed that the period of a periodic oscillator depends on the gravity field. A link was thus established between the improvement of time measurement and the knowledge of the phenomena that govern it. Since then, the performance and nature of clocks have evolved considerably. Today, atomic clocks are used in various fields that are essential to modern society, such as the realisation of international atomic time (TAI), satellite navigation (GNSS), geodesy, the traceability of trading events, etc.

In the framework of the french ANR ROYMAGE, we are interested in the contribution of a transportable optical field clock for geoscience applications by using the principle of chronometric geodesy. The idea is based on the gravitational redshift, a relativistic effect that predicts that the beat of a clock depends on the speed at which it is moving and the strength of the surrounding gravitational potential. In practice, this means that if we compare the beat of two clocks, then it is possible to directly measure a difference in gravitational potential (or a change in height) between these two clocks. This type of measurement is original because classical geodetic techniques only allow to determine the potential indirectly from gravimetric and classical levelling data.

In this work, we model the gravitational signature (potential, acceleration and tensor) of a mass anomaly as a function of its geometry, depth, size and density contrast. These synthetic simulations allow us to identify which types of structures can be detected by clock comparison measurements with a relative frequency uncertainty fixed at 10^-17-18-19 (i.e. a vertical sensitivity of less than 10 cm - 1 cm - 1 mm respectively). We are also interested in the spatial resolution required for a clock measurement to detect two mass anomalies depending on its orientation. Finally, we show that this new chronometric observable combined with gravimetry and gradiometry data could allow a better separation of the sources by adding an additional constraint thanks to the medium and long wavelength gravitational information it provides.

The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-20-CE47-0006.