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 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 .

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.

No abstract

We carried out a 26-day comparison of five simultaneously operated optical clocks and six atomic fountain clocks located at INRIM, LNE-SYRTE, NPL and PTB by using two satellite-based frequency comparison techniques: broadband Two-Way Satellite Time and Frequency Transfer (TWSTFT) and Global Positioning System Precise Point Positioning (GPS PPP). With an enhanced statistical analysis procedure taking into account correlations and gaps in the measurement data, combined overall uncertainties in the range of 1.8 × 10 −16 to 3.5 × 10 −16 for the optical clock comparisons were found. The comparison of the fountain clocks yields results with a maximum relative frequency difference of 6.9 × 10 −16 , and combined overall uncertainties in the range of 4.8 × 10 −16 to 7.7 × 10 −16 .

Summary High spatial and temporal resolution of gravity observations allows quantifying and understanding mass changes in volcanoes, geothermal or other complex geosystems. For this purpose, accurate gravity meters are required. However, transport of the gravity meters to remote study areas may affect the instrument's performance. In this work, we analyse the continuous measurements of three iGrav superconducting gravity meters (iGrav006, iGrav015 and iGrav032), before and after transport between different monitoring sites. For four months, we performed comparison measurements in a gravimetric observatory (J9, Strasbourg) where the three iGravs were subjected to the same environmental conditions. Subsequently, we transported them to Þeistareykir, a remote geothermal field in North Iceland. We examine the stability of three instrumental parameters: the calibration factors, noise levels and drift behaviour. For determining the calibration factor of each instrument, we used three methods: First, we performed relative calibration using side-by-side measurements with an observatory gravity meter (iOSG023) at J9. Second, we performed absolute calibration by comparing iGrav data and absolute gravity measurements (FG5#206) at J9 and Þeistareykir. Third, we also developed an alternative method, based on intercomparison between pairs of iGravs to check the stability of relative calibration before and after transport to Iceland. The results show that observed changes of the relative calibration factors by transport were less than or equal to 0.01 per cent. Instrumental noise levels were similar before and after transport, whereas periods of high environmental noise at the Icelandic site limited the stability of the absolute calibration measurements, with uncertainties above 0.64 per cent (6 nm s-2 V-1). The initial transient drift of the iGravs was monotonically decreasing and seemed to be unaffected by transport when the 4K operating temperatures were maintained. However, it turned out that this cold transport (at 4K) or sensor preparation procedures before transport may cause a change in the long-term quasi-linear drift rates (e.g. iGrav015 and iGrav032) and they had to be determined again after transport by absolute gravity measurements.

No abstract

Hidden matter that interacts only gravitationally would oscillate at characteristic frequencies when trapped inside of Earth. For small oscillations near the center of the Earth, these frequencies are around 300 μHz. Additionally, signatures at higher harmonics would appear because of the non-uniformity of Earth’s density. In this work, we use data from a global network of gravimeters of the International Geodynamics and Earth Tide Service (IGETS) to look for these hypothetical trapped objects. We find no evidence for such objects with masses on the order of 1014 kg or greater with an oscillation amplitude of 0.1 re. It may be possible to improve the sensitivity of the search by several orders of magnitude via better understanding of the terrestrial noise sources and more advanced data analysis. Graphical abstract