Optical clock network tracks tidal variations of the gravity potential
Authors: Kilian Stahl, Ingo Nosske, Chetan Vishwakarma, Tim Lücke, Joshua Klose, Erik Benkler, Alexander Kuhl, Shambo Mukherjee, Thomas Legero, Jochen Kronjäger, Uwe Sterr, Christian Lisdat, Sören Dörscher, Chen-Hao Feng, Matthew Y. H. Johnson, Jacques-Olivier Gaudron, Wei Huang, Jacob Tunesi, Xi Zhang, Marco Schioppo, Adam L. Parke, Ian R. Hill, Heiner Denker, Biplab Dutta, Etienne Cantin, Olivier Lopez, Anne Amy-Klein, Christian Chardonnet, Benjamin Pointard, Rodolphe Le Targat, Jérôme Lodewyck, Paul-Eric Pottie, Ichiro Ushijima, Masao Takamoto, Hidetoshi Katori, Yogeshwar B. Kale, Stefano Condio, Irene Goti, Tommaso Petrucciani, Cecilia Clivati, Simone Donadello, Filippo Levi, Davide Calonico, Marco Pizzocaro
Abstract
Gravity affects the passage of time, as described by General Relativity. On Earth, the rate of a clock as seen by a fixed observer changes by about one part in $10^{16}$ per metre in height. Chronometric levelling exploits this effect to directly measure differences in gravity potential by comparing distant clocks. It has been proposed as a complementary approach to established geodetic techniques for linking height reference systems and monitoring the terrestrial gravity potential. Experimental demonstrations have to date focused primarily on static potential differences. Yet, the potentials of the Moon, the Sun and other celestial bodies as well as the Earth's response to their tidal forcing change clock rates by several $10^{-17}$, providing a predictable test signal to demonstrate optical clock networks resolving small variations in relativistic time dilation. Here, we report chronometric observations of time-varying gravity potential differences using a network of optical clocks and phase-stabilized fibre links in Europe. Two distinct geographical configurations, with baselines of about 800 km each, result in different combinations of diurnal and semidiurnal tidal components. One comparison uses a transportable optical clock as a remote sensor. The measured rate shifts track the tidal variations, resolving the predicted signal within 1 d of measurement and agreeing with model predictions. These results extend experimental chronometric levelling from static to dynamic potential differences and highlight the need to account for the time dependence of relativistic time dilation in frequency metrology. They also open the prospect for quantum clock networks with improved stability and availability to move beyond known tides and monitor other gravity potential variations, such as those arising from surface deformation and mass redistribution in geologically or volcanically active regions.
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Potential and scientific requirements of optical clock networks for validating satellite-derived time-variable gravity dataStefan Schröder, S. Stellmer, J. Kusche · 2021 · Geophysical Journal International · cited 6 times · Not summarized yet
Potential and scientific requirements of optical clock networks evaluates clock networks for validating time-variable gravity data, the application demonstrated here.
Abstract
The Gravity Recovery and Climate Experiment (GRACE) and GRACE-FO missions have provided an unprecedented quantification of large-scale changes in the water cycle. However, it is still an open problem of how these missions’ data can be referenced to a ground truth. Meanwhile, stationary optical clocks show fractional instabilities below 10−18 when averaged over an hour, and continue to be improved in terms of stability and accuracy, uptime and transportability. The frequency of a clock is affected by the gravitational redshift, and thus depends on the local geopotential; a relative frequency change of 10−18 corresponds to a geoid height change of about 1 cm. Here we suggest that this effect c…
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Time-variable gravity potential components for optical clock comparisons and the definition of international time scalesC. Voigt, H. Denker, L. Timmen · 2016 · Metrologia · cited 96 times · Not summarized yet
Time-variable gravity potential components analyzes gravity variations relevant to optical-clock comparisons and international time scales, which this paper measures.
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Geopotential measurements with synchronously linked optical lattice clocksTetsushi Takano, M. Takamoto, I. Ushijima et al. · 2016 · Nature Photonics · cited 222 times · Not summarized yet
Geopotential measurements with synchronously linked optical lattice clocks demonstrates chronometric levelling between linked clocks, but measures a static height difference.
Abstract
Real-time geopotential measurements with two synchronously linked optical lattice clocks are demonstrated. A height difference between the two clocks separated by 15 km is determined, with an uncertainty of 5 cm, by means of a gravitational redshift. According to Einstein's theory of relativity, the passage of time changes in a gravitational field1,2. On Earth, raising a clock by 1 cm increases its apparent tick rate by 1.1 parts in 1018, allowing chronometric levelling3 through comparison of optical clocks1,4,5. Here, we demonstrate such geopotential measurements by determining the height difference of master and slave clocks separated by 15 km with an uncertainty of 5 cm. A subharmonic of …
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Ground-based optical atomic clocks as a tool to monitor vertical surface motionR. Bondarescu, Andreas Scharer, A. Lundgren et al. · 2015 · Geophysical Journal International · cited 55 times · Not summarized yet
Ground-based optical atomic clocks as a tool to monitor vertical surface motion discusses clock networks sensing geophysical potential changes, including vertical motion.
Abstract
SUMMARY According to general relativity, a clock experiencing a shift in the gravitational potential �U will measure a frequency change given byf/f ≈ �U/c 2 . The best clocks are optical clocks. After about 7 hr of integration they reach stabilities off/f ∼ 10 −18 and can be used to detect changes in the gravitational potential that correspond to vertical displacements of the centimetre level. At this level of performance, ground-based atomic clock networks emerge as a tool that is complementary to existing technology for monitoring a wide range of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clock's position due to magmatic, pos…
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Geodesy and metrology with a transportable optical clockJ. Grotti, S. Koller, S. Vogt et al. · 2017 · Nature Physics · cited 468 times · Not summarized yet
Geodesy and metrology with a transportable optical clock demonstrates field measurements of gravity potential using a transportable clock, also used here.
Abstract
Optical atomic clocks, due to their unprecedented stability1–3 and uncertainty3–6, are already being used to test physical theories7,8 and herald a revision of the International System of Units9,10. However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy11, a major challenge remains: their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations12–14. Here, we report the first field measurement campaign with a transportable 87Sr optical lattice clock12. We use it to determine the gravity potential difference between the middle of a mountain and a locatio…
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Long-distance chronometric leveling with a portable optical clockJ. Grotti, I. Nosske, S. Koller et al. · 2023 · Physical Review Applied · cited 35 times · Not summarized yet
Long-distance chronometric leveling with a portable optical clock measures a static geopotential difference over a long fibre-linked baseline, preceding this dynamic measurement.
Abstract
We have measured the geopotential difference between two locations separated by 457 km by comparison of two optical lattice clocks via an interferometric fiber link, utilizing the gravitational redshift of the clock transition frequency. The 87Sr clocks have been compared side-by-side before and after one of the clocks was moved to the remote location. The chronometrically measured geopotential difference of 3918.1(2.6)m2s−2 agrees with an independent geodetic determination of 3915.88(0.30)m2s−2. The uncertainty of the chronometric geopotential difference is equivalent to an uncertainty of 27cm in height. Published by the American Physical Society 2024
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Exploring potential applications of optical lattice clocks in a plate subduction zoneYoshiyuki Tanaka, H. Katori · 2021 · Journal of Geodesy · cited 23 times · Not summarized yet
Exploring potential applications of optical lattice clocks in a plate subduction zone considers using clock sensitivity to monitor seismic and volcanic changes.
Abstract
Optical clocks improved the accuracy of state-of-the-art cesium clocks by more than two orders of magnitude and enabled frequency comparison with a fractional uncertainty of one part in 1018. Gravitational redshift of two such clocks allows determining their height difference with an uncertainty of 1 cm. In Europe, chronometric leveling has been extensively conducted for unifying the height reference systems. Temporal response of the leveling, which affords monitoring a cm height variation within hours of averaging time, may offer new opportunities to explore seismology and volcanology. Superb stability of optical lattice clocks will be best used for such applications. This article outlines …
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Atomic clocks for geodesyT. Mehlstäubler, G. Grosche, C. Lisdat et al. · 2018 · Reports on progress in physics. Physical Society · cited 237 times · Not summarized yet
Atomic clocks for geodesy reviews optical clocks and frequency transfer for geodetic measurements.
Abstract
We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10−17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein’s general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international cl…
Prior work it builds on
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Chronometric Geodesy: Methods and ApplicationsP. Delva, H. Denker, G. Lion · 2018 · Fundamental Theories of Physics · cited 24 times · Not summarized yet
Chronometric Geodesy: Methods and Applications surveys methods for using distant clock-frequency comparisons to study the gravity field.
Abstract
The theory of general relativity was born more than one hundred years ago, and since the beginning has striking prediction success. The gravitational redshift effect discovered by Einstein must be taken into account when comparing the frequencies of distant clocks. However, instead of using our knowledge of the Earth’s gravitational field to predict frequency shifts between distant clocks, one can revert the problem and ask if the measurement of frequency shifts between distant clocks can improve our knowledge of the gravitational field. This is known as chronometric geodesy. Since the beginning of the atomic time era in 1955, the accuracy and stability of atomic clocks were constantly ameli…
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Gravitational wave detection with optical lattice atomic clocksS. Kolkowitz, I. Pikovski, N. Langellier et al. · 2016 · Physical Review D · cited 332 times · Not summarized yet
Gravitational wave detection with optical lattice atomic clocks proposes space-based clock comparisons to detect gravitational waves rather than terrestrial tidal potential changes.
Abstract
We propose a space-based gravitational wave (GW) detector consisting of two spatially separated, drag-free satellites sharing ultrastable optical laser light over a single baseline. Each satellite contains an optical lattice atomic clock, which serves as a sensitive, narrowband detector of the local frequency of the shared laser light. A synchronized two-clock comparison between the satellites will be sensitive to the effective Doppler shifts induced by incident GWs at a level competitive with other proposed space-based GW detectors, while providing complementary features. The detected signal is a differential frequency shift of the shared laser light due to the relative velocity of the sate…
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Test of general relativity by a pair of transportable optical lattice clocksM. Takamoto, I. Ushijima, N. Ohmae et al. · 2020 · Nature Photonics · cited 462 times · Not summarized yet
Test of general relativity by a pair of transportable optical lattice clocks uses transportable clocks to test relativistic frequency shifts.
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Gravitational-wave astronomy with a space-based optical clock networkDhruva Ganapathy, Divya Singh, Sammith Singamsetty et al. · 2026 · Physical Review D · cited 2 times · Not summarized yet
Gravitational-wave astronomy with a space-based optical clock network considers clock networks for detecting astrophysical gravitational waves.
Abstract
Since the first detection of a merging binary black hole system a decade ago, gravitational-wave astronomy has emerged as a powerful tool for astrophysics. Future space-based observatories, such as the Laser Interferometer Space Antenna (LISA), will unlock the millihertz (mHz) band, which remains entirely inaccessible to ground-based detectors due to terrestrial noise. In parallel, proposed atom-based gravitational-wave detectors, specifically those based on space-based optical clocks and atom interferometers, offer capabilities that are unique and complementary to traditional optical interferometers. Their highly tunable character enables sensitive measurements across a broad frequency band…
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Frequency stability and phase noise measurements of a 5,860 km-long intercontinental seafloor optical fibre cableG. Marra, P. Gaynor, M. Cantono et al. · 2022 · cited 1 time · Not summarized yet
Frequency stability and phase noise measurements of a 5,860 km-long intercontinental seafloor optical fibre cable characterizes long-distance frequency transfer needed for clock comparisons.
Abstract
Optical clock comparison via optical fibre links has been achieved over continental scales, but has not yet been demonstrated intercontinentally. The transfer of ultra-stable optical frequencies over transoceanic distances is a challenging task, as the seafloor cable architecture prevents the use of environmental noise suppression techniques currently employed on land-based metrological links. As a fundamental first step towards devising suitable frequency transfer techniques to enable future clock comparison on a global scale, here we show the free-running frequency stability and phase noise measurements of a transatlantic seafloor optical link between the UK and Canada. To the best of our …
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