The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability 1,2,3 and uncertainty, 4,5,6,7 are already being used to test physical theories 8,9 and herald a revision of the International System of units (SI). 10,11 However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, 12 a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. 13,14,15 Here we report the first field measurement campaign performed with a ubiquitously applicable 87 Sr optical lattice clock. 13 We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a 171 Yb lattice clock 16 also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.The application of clocks in geodesy fulfils long-standing proposals to interpret a measurement of the fractional relativistic redshift Δνrel/ν0 to determine the gravity potential difference ΔU = c 2 Δνrel/ν0 between clocks at two sites (c being the speed of light). 12 National geodetic height systems based on classical terrestrial and satellite-based measurements exhibit discrepancies at the decimetre level. 17 Optical clocks, combined with high performance frequency dissemination techniques 18,19 offer an attractive way to resolve these discrepancies, as they combine the advantage of high spectral resolution with small error accumulation over long distances. 18,20 However, to achieve competitive capability requires high clock performance: a fractional frequency accuracy of 1×10 17 corresponds to a resolution of about 10 cm in height. Furthermore, it is important to realize that the sideby-side frequency ratio has to be known to determine the remote frequency shift Δνrel. Taking the uncertainty budgets of optical clocks for granted, harbours the possibility of errors, because very few have been verified experimentally to the low 10 17 region or beyond. 5,7,18,21 A transportable optical clock not only increases the flexibility in measurement sites but mitigates the risk of undetected errors by enabling local calibrations to be performed.The test site chosen for our demonstration of chronometric levelling 12 with optical clocks was the Laboratoire Souterrain de Modane (LSM) in France, with the Italian metrology institute INRIM in Torino serving as the reference site. The height difference between the two sites is approximately 1000 m, corresponding to a fractional redshift of about 10 -13 . From a geodetic point of view, LSM is a challenging and interesting location in which to perform such measurements: firstly, it is located in the middl...

The 8th International Comparison of Absolute Gravimeters (ICAG2009) took place at the headquarters of the International Bureau of Weights and Measures (BIPM) from September to October 2009. It was the first ICAG organized as a key comparison in the framework of the CIPM Mutual Recognition Arrangement of the International Committee for Weights and Measures (CIPM MRA) (CIPM 1999). ICAG2009 was composed of a Key Comparison (KC) as defined by the CIPM MRA, organized by the Consultative Committee for Mass and Related Quantities (CCM) and designated as CCM.G-K1. Participating gravimeters and their operators came from national metrology institutes (NMIs) or their designated institutes (DIs) as defined by the CIPM MRA. A Pilot Study (PS) was run in parallel in order to include gravimeters and their operators from other institutes which, while not signatories of the CIPM MRA, nevertheless play important roles in international gravimetry measurements. The aim of the CIPM MRA is to have international acceptance of the measurement capabilities of the participating institutes in various fields of metrology. The results of CCM.G-K1 thus constitute an accurate and consistent gravity reference traceable to the SI (International System of Units), which can be used as the global basis for geodetic, geophysical and metrological observations of gravity. The measurements performed afterwards by the KC participants can be referred to the international metrological reference, i.e. they are SI-traceable. The ICAG2009 was complemented by a number of associated measurements: the Relative Gravity Campaign (RGC2009), high-precision levelling and an accurate gravity survey in support of the BIPM watt balance project. The major measurements took place at the BIPM between July and October 2009. Altogether 24 institutes with 22 absolute gravimeters (one of the 22 AGs was ultimately withdrawn) and nine relative gravimeters participated in the ICAG/RGC campaign. This paper is focused on the absolute gravity campaign. We review the history of the ICAGs and present the organization, data processing and the final results of the ICAG2009. After almost thirty years of hosting eight successive ICAGs, the CIPM decided to transfer the responsibility for piloting the future ICAGs to NMIs, although maintaining a supervisory role through its Consultative Committee for Mass and Related Quantities.

We report a comparison between two absolute gravimeters: the LNE-SYRTE cold atom gravimeter and FG5#220 of Leibniz Universität of Hannover. They rely on different principles of operation: atomic and optical interferometry. Both are movable which enabled them to participate in the last International Comparison of Absolute Gravimeters (ICAG'09) at BIPM. Immediately after, their bilateral comparison took place in the LNE watt balance laboratory and showed an agreement of (4.3 ± 6.4) µGal.

The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in 10 18 level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about 0.1 m 2 s −2 , equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about 2 × 10 −18 .

For up-to-date absolute gravimeters, the trajectory of the test mass during a free-fall experiment (drop) is about 20 cm along the vertical, and the corresponding gravity change is about 60 × 10 −8 m s −2 . The reference height of the derived free-fall acceleration g has to be defined with an accuracy of 1 mm to 2 mm within the dropping distance to preserve the accuracy of the measurement system (e.g. FG5: 1 × 10 −8 m s −2 to 2 × 10 −8 m s −2 ). The equation of motion comprises a vertical gravity gradient to take the height dependence of g into account. In general, a linear vertical gravity gradient γ is introduced that has been measured by relative gravimeters. In that case, the g-value refers to the origin of the coordinate system (z = 0), which is normally the starting position of the drop.In the case of an unknown or uncertain gradient we recommend an alternative approach. A simple parabolic equation (assumption γ = 0) can be used to evaluate the time/distance data pairs, and later these g-determinations have to be corrected for the vertical gravity gradient using the effective measurement height. The solution presented is not restricted to low initial velocities. It considers time/distance measurements equally spaced in distance. Also, in extreme cases, unknown non-linearities within the vertical gravity gradient do not significantly affect the result of the absolute gravity determination.

The latest generation of optical atomic clocks is approaching the level of one part in 10 18 in terms of frequency stability and uncertainty. For clock comparisons and the definition of international time scales, a relativistic redshift effect of the clock frequencies has to be taken into account at a corresponding uncertainty level of about 0.1 m 2 s −2 and 0.01 m in terms of gravity potential and height, respectively. Besides the predominant static part of the gravity potential, temporal variations must be considered in order to avoid systematic frequency shifts. Time-variable gravity potential components induced by tides and non-tidal mass redistributions are investigated with regard to the level of one part in 10 18 . The magnitudes and dominant time periods of the individual gravity potential contributions are investigated globally and for specific laboratory sites together with the related uncertainty estimates. The basics of the computation methods are presented along with the applied models, data sets and software. Solid Earth tides contribute by far the most dominant signal with a global maximum amplitude of 4.2 m 2 s −2 for the potential and a range (maximum-to-minimum) of up to 1.3 and 10.0 m 2 s −2 in terms of potential differences between specific laboratories over continental and intercontinental scales, respectively. Amplitudes of the ocean tidal loading potential can amount up to 1.25 m 2 s −2 , while the range of the potential between specific laboratories is 0.3 and 1.1 m 2 s −2 over continental and intercontinental scales, respectively. These are the only two contributors being relevant at a 10 −17 level. However, several other time-variable potential effects can particularly affect clock comparisons at the 10 −18 level. Besides solid Earth pole tides, these are non-tidal mass redistributions in the atmosphere, the oceans and the continental water storage.

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