SFB 1128:  Relativistic Geodesy and Gravimetry with Quantum Sensors - Modelling, Geo-Metrology and Future Technology (geo-Q)

Final Report Abstract

Climate change is one of the greatest challenge of the present time. We are only able to understand the processes relevant for these changes if we analyse the temporal and spatial variations of the gravitational field of the Earth. Gravitational data allow quantifying mass variations such as the mass loss of polar ice sheets, the contribution of mass influx to sea level rise, and changes in the hydrological cycle. Gravitational data are also urgently needed to improve the reference systems used in geodesy and Earth observation. The scientific challenges are threefold: • to determine and monitor global and regional gravity and mass variations from processes that cannot be resolved with the accuracy of current gravitational measurement techniques; • to determine gravity variations with the spatial resolution that is needed for a detailed understanding of mass redistribution and for the separation of sources and mechanisms; • to provide an accurate gravity reference for monitoring processes over long time scales as a basis to reliable quantify both long-term changes and rapid variations. To meet these challenges, new concepts for observing mass variations are required. geo-Q has integrated expertise from geodesy and physics in a unique constellation. geo-Q studied and developed fundamentally new sensors and measurement techniques based on quantum metrology. We investigated laser interferometric systems for ranging between test masses in orbit for satellite gravimetry, with noise levels of nanometers over large distances, and picometers locally, in configurations that allow suitable spatial and temporal sampling of gravity variations. We have succeeded in characterising major noise sources in spaceborne laser interferometry and developed tools to mitigate them. Here, geo-Q crucially benefited from knowledge transfer from the very successful mission “LISA Pathfinder (LPF)” (2015 - 2017) to gravity field missions. The mission GRACE Follow-On (GRACE-FO) (launched in 2018) already profits from this cross-fertilisation. Experiences from geo-Q will be essential to future satellite gravimetry concepts. In geo-Q we also studied and developed atomic gravity sensors for rapid and very precise gravity sensing, based on matter wave interferometry with atoms in the nano-Kelvin to pico-Kelvin temperature regime. These developments enable both compact, mobile devices for field campaigns and large-scale stationary devices for extreme precision. While the former allows for new strategies for local and regional gravity surveys, the latter is able to serve as new gravity standard in the future. geo-Q heralded a paradigm change in atom interferometry, demonstrating a quantum gravimeter employing interferometry with Bose-Einstein condensates created on atom chips. As a third pillar, geo-Q pioneered the concept of relativistic geodesy and addressed its practical application for the realisation of physical height systems and gravity field observations. Key is the observation and comparison of the gravitational frequency redshift over long distances on Earth to determine gravitational potential differences in geodetic networks, using transportable optical atomic clocks and frequency transfer in optical fibre networks. Successful measurements were obtained between Paris and Braunschweig at the 10^−17 level for the relative frequency difference. Along with the research on measurement systems and techniques, where more and more accurate data have been obtained, we also put the analysis models on a sound theoretical basis. This required dedicated relativistic modelling of the various involved gravity field quantities and measurement concepts. A general relativistic definition of the geoid has been developed and it was shown that the resulting “isochronometric surfaces” obtained from clock measurements are mathematically equivalent to a definition based on the levelling approach. In preparation for networks of clocks which can enable stabilisation of height systems, synthetic clock data has been used to identify how many clocks (≥ 4) are required to improve the solution when combined with classical geodetic observables. Furthermore, a framework has been developed to test general relativity through clocks. These clocks and concepts enable new developments for the needs in geodesy, such as unifying height systems and gravity field recovery in the future. Geodetic projects supported the development of novel concepts meeting the requirements on Earth observation and studied the best possible exploitation of these new data. We now know how to deal with disturbing signals in inter-satellite range-rate measurements and are also able to handle potentially disturbing signals affecting clock measurements. geo-Q succeeded in determining a highly accurate static gravity field by combining spaceborne gravimetry and terrestrial data. Our development and realisation of new concepts for observing mass variations in geo-Q enables the acquisition of crucial quantitative input for climate change research with corresponding enormous impact on the whole field of geoscience.

Publications

• (2014). “Generalized gravitomagnetic clock effect”. In: Physical Review D Vol. 90, No. 4, p. 044059
  Hackmann E. and Lämmerzahl C.
  
• (2015). “A high-flux BEC source for mobile atom interferometers”. In: New Journal of Physics Vol. 17, No. 6, p. 065001
  Rudolph J., Herr W., Grzeschik C., Sternke T., Grote A., Popp M., Becker D., Müntinga H., Ahlers H., Peters A., Lämmerzahl C., Sengstock K., Gaaloul N., Ertmer W., and Rasel E. M.
  
• (2015). “Species-selective lattice launch for precision atom interferometry”. In: New Journal of Physics Vol. 17, No. 12, p. 123002
  Chamakhi R., Ahlers H., Telmini M., Schubert C., Rasel E. M., and Gaaloul N.
  
• (2015). “Testing the universality of free fall with rubidium and ytterbium in a very large baseline atom interferometer”. In: New Journal of Physics Vol. 17, No. 3, p. 035011
  Hartwig J., Abend S., Schubert C., Schlippert D., Ahlers H., Posso-Trujillo K., Gaaloul N., Ertmer W., and Rasel E. M.
  
• (2017). Global Gravity Field Modeling from Satellite-to-Satellite Tracking Data. Lecture Notes in Earth System Sciences. Springer
  Naeimi M. and Flury J., eds.
  
• (2016). “A clock network for geodesy and fundamental science”. In: Nature Communications Vol. 7, p. 12443
  Lisdat C., Grosche G., Quintin N., Shi C., Raupach S., Grebing C., Nicolodi D., Stefani F., Al-Masoudi A .and Dörscher S., Häfner S., Robyr J.-L., Chiodo N., Bilicki S., Bookjans E., Koczwara A., Koke S., Kuhl A., Wiotte F., Meynadier F., Camisard E., Abgrall M., Lours M., Legero T., Schnatz H., Sterr U., et al.
  
• (2016). “Atom-chip fountain gravimeter”. In: Physical Review Letters Vol. 117, No. 20, p. 203003
  Abend S., Gebbe M., Gersemann M., Ahlers H., Müntinga H., Giese E., Gaaloul N., Schubert C., Lämmerzahl C., Ertmer W., Schleich W. P., and Rasel E. M.
  
• (2016). “Experimental demonstration of deep frequency modulation interferometry”. In: Optics Express Vol. 24, No. 2, pp. 1676–1684
  Isleif K.-S., Gerberding O., Schwarze T. S., Mehmet M., Heinzel G., and Cervantes F. G.
  
• (2016). “Experimental demonstration of reduced tilt-to-length coupling by a two-lens imaging system”. In: Optics Express Vol. 24, No. 10, pp. 10466–10475
  Schuster S., Tröbs M., Wanner G., and Heinzel G.
  
• (2016). “Time-variable gravity potential components for optical clock comparisons and the definition of international time scales”. In: Metrologia Vol. 53, No. 6, pp. 1365–1383
  Voigt C., Denker H., and Timmen L.
  
• (2017). “A Data-Driven Approach for Repairing the Hydrological Catchment Signal Damage Due to Filtering of GRACE Products”. In: Water Resources Research Vol. 53, No. 11, pp. 9824–9844
  Vishwakarma B. D., Horwath M., Devaraju B., Groh A., and Sneeuw N.
  
• (2017). “Definition of the relativistic geoid in terms of isochronometric surfaces”. In: Physical Review D Vol. 95, No. 10, p. 104037
  Philipp D., Perlick V., Pützfeld D., Hackmann E., and Lämmerzahl C.
  
• (2017). “Geodetic methods to determine the relativistic redshift at the level of 10−18 in the context of international timescales – A review and practical results”. In: Journal of Geodesy Vol. 92, No. 5, pp. 487–516
  Denker H., Timmen L., Voigt C., Weyers S., Peik E., Margolis H., Delva P., Wolf P., and Petit G.
  
• (2017). “High Performance Clocks and Gravity Field Determination”. In: Space Science Reviews Vol. 214, No. 1
  Müller J., Dirkx D., Kopeikin S. M., Lion G., Panet I., Petit G., and Visser P. N. A. M.
  
• (2017). “Laser-Frequency Stabilization via a Quasimonolithic Mach-Zehnder Interferometer with Arms of Unequal Length and Balanced dc Readout”. In: Physical Review Applied Vol. 7, No. 2, p. 024027
  Gerberding O., Isleif K.-S., Mehmet M., Danzmann K., and Heinzel G.
  
• (2017). “Possible alternative acquisition scheme for the gravity recovery and climate experiment follow-on-type mission”. In: Applied Optics Vol. 56, No. 5, pp. 1495–1500
  Luo Z., Wang Q., Mahrdt C., Görth A., and Heinzel G.
  
• (2017). “Test of special relativity using a fiber network of optical clocks”. In: Physical Review Letters Vol. 118, No. 22, p. 221102
  Delva P., Lodewyck J., Bilicki S., Bookjans E., Vallet G., Le Targat R., Pottie P.-E., Guerlin C., Meynadier F., Le Poncin-Lafitte C., Lopez O., Amy-Klein A., Lee W.-K., Quintin N., Lisdat C., Al-Masoudi A., Dörscher S., Grebing C., Grosche G., Kuhl A., Raupach S., Sterr U., Hill I. R.and Hobson R., Bowden W., Kronjäger J., et al.
  
• (2017). “Transportable Optical Lattice Clock with 7 × 10−17 Uncertainty”. In: Physical Review Letters Vol. 118, No. 7, p. 073601
  Koller S., Grotti J., Al-Masoudi A., Dörscher S., Häfner S., Sterr U., and Lisdat C.
  
• (2018). “A highly stable monolithic enhancement cavity for second harmonic generation in the ultraviolet”. In: Review of Scientific Instruments Vol. 89, No. 1, p. 013106
  Hannig S., Mielke J., Fenske J. A., Misera M., Beev N., Ospelkaus C., and Schmidt P. O.
  
• (2018). “Analysis of Attitude Errors in GRACE Range-Rate Residuals - A Comparison Between SCA1B and the Fused Attitude Product (SCA1B+ACC1B)”. In: IEEE Sensors Letters Vol. 2, No. 2, pp. 1–4
  Goswami S., Klinger B., Weigelt M., and Mayer-Gurr T.
  
• (2018). “Analysis of GRACE range-rate residuals with focus on KBR instrument system noise”. In: Advances in Space Research Vol. 62, No. 2, pp. 304–316
  Goswami S., Devaraju B., Weigelt M., and Mayer-Gürr T.
  
• (2018). “Analysis of non-tidal ocean loading for gravitational potential observations in northern Europe”. In: Journal of Geodynamics Vol. 119, pp. 23–28
  Leßmann L. and Müller J.
  
• (2018). “Atomic clocks for geodesy”. In: Reports on Progress in Physics Vol. 81, No. 6, p. 064401
  Mehlstäubler T. E., Grosche G., Lisdat C., Schmidt P. O., and Denker H.
  
• (2018). “Clock networks for height system unification: a simulation study”. In: Geophysical Journal International Vol. 216, No. 3, pp. 1594–1607
  Wu H., Müller J., and Lämmerzahl C.
  
• (2018). “Experimental and theoretical investigation of a multimode cooling scheme using multiple electromagnetically-induced-transparency resonances”. In: Phys. Rev. A Vol. 98 (2), p. 023424
  Scharnhorst N., Cerrillo J., Kramer J., Leroux I. D., Wübbena J. B., Retzker A., and Schmidt P. O.
  
• (2018). “Geodesy and metrology with a transportable optical clock”. In: Nature Physics Vol. 14, No. 5, pp. 437–441
  Grotti J., Koller S., Vogt S., Häfner S., Sterr U., Lisdat C., Denker H., Voigt C., Timmen L., Rolland A., Baynes F. N., Margolis H. S., Zampaolo M., Thoumany P., Pizzocaro M., Rauf B., Bregolin F., Tampellini A., Barbieri P., Zucco M., Costanzo G. A., Clivati C., Levi F., and Calonico D.
  
• (2018). “Gravitational clock compass in general relativity”. In: Phys. Rev. D Vol. 98, No. 2 (2), p. 024032
  Puetzfeld D., Obukhov Y. N., and Lämmerzahl C.
  
• (2018). “Line of sight calibration for the laser ranging interferometer on-board the GRACE Follow-On mission: on-ground experimental validation”. In: Opt. Express Vol. 26, No. 20, pp. 25892–25908
  Koch A., Sanjuan J., Gohlke M., Mahrdt C., Brause N., Braxmaier C., and Heinzel G.
  
• (2018). “Modeling approaches for precise relativistic orbits: Analytical, Lie-series, and pN approximation”. In: Advances in Space Research Vol. 62, No. 4, pp. 921–934
  Philipp D., Woeske F., Biskupek L., Hackmann E., Mai E., List M., Lämmerzahl C., and Rievers B.
  
• (2018). “Reducing tilt-to-length coupling for the LISA test mass interferometer”. In: Classical and Quantum Gravity Vol. 35, No. 10
  Troebs M., Schuster S., Lieser M., Zwetz M., Chwalla M., Danzmann K., Barranco G. F., Fitzsimons E. D., Gerberding O., Heinzel G., Killow C. J., Perreur-Lloyd M., Robertson D. I., Schwarze T. S., Wanner G., and Ward H.
  
• (2018). “Simulation-based evaluation of a cold atom interferometry gradiometer concept for gravity field recovery”. In: Advances in Space Research Vol. 61, pp. 1307–132
  Douch K., Wu H., Schubert C., Müller J., and Pereira dos Santos F.
  
• (2018). “Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbit”. In: Phys. Rev. Lett. Vol. 121 (23), p. 231102
  Herrmann S., Finke F., Lülf M., Kichakova O., Puetzfeld D., Knickmann D., List M., Rievers B., Giorgi G., Günther C., Dittus H., Prieto-Cerdeira R., Dilssner F., Gonzalez F., Schönemann E., Ventura-Traveset J., and Lämmerzahl C.
  
• (2018). “Towards the LISA backlink: experiment design for comparing optical phase reference distribution systems”. In: Classical and Quantum Gravity Vol. 35, No. 8
  Isleif K.-S., Bischof L., Ast S., Penkert D., Schwarze T. S., Barranco G. F., Zwetz M., Veith S., Hennig J.-S., Troebs M., Reiche J., Gerberding O., Danzmann K., and Heinzel G.
  
• (May 2018). “Fast manipulation of Bose–Einstein condensates with an atom chip”. In: New Journal of Physics Vol. 20, No. 5, p. 055002
  Corgier R., Amri S., Herr W., Ahlers H., Rudolph J., Guéry-Odelin D., Rasel E. M., Charron E., and Gaaloul N.
  
• (2019). “A comparison of fixed-and free-positioned point mass methods for regional gravity field modeling”. In: Journal of Geodynamics Vol. 125, pp. 32–47
  Lin M., Denker H., and Müller J.
  
• (2019). “Atomic source selection in space-borne gravitational wave detection”. In: New Journal of Physics Vol. 21, No. 6, p. 063030
  Loriani S., Schlippert D., Schubert C., Abend S., Ahlers H., Ertmer W., Rudolph J., Hogan J. M., Kasevich M. A., Rasel E. M., and Gaaloul N.
  
• (2019). “Compact Multifringe Interferometry with Subpicometer Precision”. In: Physical Review Applied Vol. 12, No. 3
  Isleif K.-S., Heinzel G., Mehmet M., and Gerberding O.
  
• (2019). “Grace Accelerometer Calibration by High Precision Non-gravitational Force Modeling”. In: Advances in Space Research Vol. 63, No. 3, pp. 1318–1335
  Wöske F., Kato T., Rievers B., and List M.
  
• (2019). “Picometer-Stable Hexagonal Optical Bench to Verify LISA Phase Extraction Linearity and Precision”. In: Physical Review Letters Vol. 122, No. 8
  Schwarze T. S., Barranco G. F., Penkert D., Kaufer M., Gerberding O., and Heinzel G.
  
• (2019). “Towards a transportable aluminium ion quantum logic optical clock”. In: Review of Scientific Instruments Vol. 90, No. 5, p. 053204
  Hannig S., Pelzer L., Scharnhorst N., Kramer J., Stepanova M., Xu Z. T., Spethmann N., Leroux I. D., Mehlstäubler T. E., and Schmidt P. O.
  

Completed projects