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Formulation of Determining the Gravity Potential Difference Using Ultra-High Precise Clocks via Optical Fiber Frequency Transfer Technique

  • Ziyu Shen
  • Wen-Bin Shen
  • Zhao Peng
  • Tao Liu
  • Shougang Zhang
  • Dingbo Chao
Article
  • 19 Downloads

Abstract

Based on gravity frequency shift effect predicted by general relativity theory, this study discusses an approach for determining the gravity potential (geopotential) difference between arbitrary two points P and Q by remote comparison of two precise optical clocks via optical fiber frequency transfer. After synchronization, by measuring the signal’s frequency shift based upon the comparison of bidirectional frequency signals from P and Q oscillators connected with two optical atomic clocks via remote optical fiber frequency transfer technique, the geopotential difference between the two points could be determined, and its accuracy depends on the stabilities of the optical clocks and the frequency transfer comparison technique. Due to the fact that the present stability of optical clocks achieves 1.6×10-18 and the present frequency transfer comparison via optical fiber provides stabilities as high as 10-19 level, this approach is prospective to determine geopotential difference with an equivalent accuracy of 1.5 cm. In addition, since points P and Q are quite arbitrary, this approach may provide an alternative way to determine the geopotential over a continent, and prospective potential to unify a regional height datum system.

Key Words

gravity frequency shift optical fiber frequency transfer optical clock gravity potential 

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Notes

Acknowledgments

We sincerely thank three anonymous reviewers, who’s valuable comments and suggestions greatly improved the manuscript. This study was supported by the National Natural Science Foundation of China (Nos. 41631072, 41721003, 41574007, and 41429401), the Discipline Innovative Engineering Plan of Modern Geodesy and Geodynamics (No. B17033), the DAAD Thematic Network Project (No. 57173947), and the International Space Science Institute (ISSI) 2017–2019. The final publication is available at Springer via https://doi.org/10.1007/s12583-018-0834-0.

References Cited

  1. Akatsuka, T., Takamoto, M., Katori, H., 2008. Optical Lattice Clocks with Non-Interacting Bosons and Fermions. Nature Physics, 4(12): 954–959. https://doi.org/10.1038/nphys1108 CrossRefGoogle Scholar
  2. Bjerhammar, A., 1985. On a Relativistic Geodesy. Bulletin Géodésique, 59(3): 207–220. https://doi.org/10.1007/bf02520327 CrossRefGoogle Scholar
  3. Bloom, B. J., Nicholson, T. L., Williams, J. R., et al., 2014. An Optical Lattice Clock with Accuracy and Stability at the 10–18 Level. Nature, 506(7486): 71–75. https://doi.org/10.1038/nature12941 CrossRefGoogle Scholar
  4. Chou, C. W., Hume, D. B., Koelemeij, J., et al., 2010a. Frequency Comparison of Two High-Accuracy Al+ Optical Clocks. Physical Review Letters, 104(7): 070802. https://doi.org/10.1103/physrevlett.104.070802 CrossRefGoogle Scholar
  5. Chou, C. W., Hume, D. B., Rosenband, T., et al., 2010b. Optical Clocks and Relativity. Science, 329(5999): 1630–1633. https://doi.org/10.1126/science.1192720 CrossRefGoogle Scholar
  6. Diddams, S. A., Bergquist, J. C., Jefferts, S. R., et al., 2004. Standards of Time and Frequency at the Outset of the 21st Century. Science, 306(5700): 1318–1324. https://doi.org/10.1126/science.1102330 CrossRefGoogle Scholar
  7. Diddams, S. A., Udem, T., Bergquist, J. C., et al., 2001. An Optical Clock Based on a Single Trapped 199Hg+ Ion. Science, 293(5531): 825–828. https://doi.org/10.1126/science.1061171 CrossRefGoogle Scholar
  8. Droste, S., Ozimek, F., Udem, T., et al., 2013. Optical-Frequency Transfer over a Single-Span 1 840 km Fiber Link. Physical Review Letters, 111(11): 110801. https://doi.org/10.1103/physrevlett.111.110801 CrossRefGoogle Scholar
  9. Dziewonski, A. M., Anderson, D. L., 1981. Preliminary Reference Earth Model. Physics of the Earth and Planetary Interiors, 25(4): 297–356. https://doi.org/10.1016/0031-9201(81)90046-7 CrossRefGoogle Scholar
  10. Flury, J., 2016. Relativistic Geodesy. Journal of Physics Conference Series, 723(1): 012051CrossRefGoogle Scholar
  11. Grosche, G., Terra, O., Predehl, K., et al., 2009. Optical Frequency Transfer via 146 km Fiber Link with 10–19 Relative Accuracy. Optics Letters, 34(15): 2270–2272. https://doi.org/10.13039/501100000844 CrossRefGoogle Scholar
  12. Grotti, J., Koller, S., Vogt, S., et al., 2018. Geodesy and Metrology with a Transportable Optical Clock. Nature Physics, 14(5): 437–441. https://doi.org/10.1038/s41567-017-0042-3 CrossRefGoogle Scholar
  13. Guena, J., Abgrall, M., Rovera, D., et al., 2012. Progress in Atomic Fountains at LNE-SYRTE. Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, 59(3): 391–409. https://doi.org/10.1109/tuffc.2012.2208 CrossRefGoogle Scholar
  14. Heiskanen, W. A., Moritz, H., 1967. Physical Geodesy. Freeman and Company, San Francisco Google Scholar
  15. Hinkley, N., Sherman, J. A., Phillips, N. B., et al., 2013. An Atomic Clock with 10–18 Instability. Science, 341(6151): 1215–1218. https://doi.org/10.1126/science.1240420 CrossRefGoogle Scholar
  16. Hofmann-Wellenhof, B., Moritz, H., 2006. Physical Geodesy. Springer Google Scholar
  17. Huntemann, N., Okhapkin, M., Lipphardt, B., et al., 2012. High-Accuracy Optical Clock Based on the Octupole Transition in 171Yb+. Physical Review Letters, 108(9): 090801. https://doi.org/10.1103/physrevlett.108.090801 CrossRefGoogle Scholar
  18. Jiang, H., Kéfélian, F., Crane, S., et al., 2008. Long-Distance Frequency Transfer over an Urban Fiber Link Using Optical Phase Stabilization. Journal of the Optical Society of America B, 25(12): 2029–2035. https://doi.org/10.13039/501100001665 CrossRefGoogle Scholar
  19. Katila, T., Riski, K. J., 1981. Measurement of the Interaction between Electromagnetic Radiation and Gravitational Field Using 67Zn Mössbauer Spectroscopy. Physics Letters A, 83(2): 51–54. https://doi.org/10.1016/0375-9601(81)90062-1 CrossRefGoogle Scholar
  20. Katori, H., 2011. Optical Lattice Clocks and Quantum Metrology. Nature Photonics, 5(4): 203–210. https://doi.org/10.1038/nphoton.2011.45 CrossRefGoogle Scholar
  21. Kéfélian, F., Lopez, O., Jiang, H. F., et al., 2009. High-Resolution Optical Frequency Dissemination on a Telecommunications Network with Data Traffic. Optics Letters, 34(10): 1573–1575. https://doi.org/10.13039/501100001665 CrossRefGoogle Scholar
  22. Li, W. Y., Liu, Y. X., Li, B., et al., 2016. Hydrocarbon Exploration in the South Yellow Sea Based on Airborne Gravity, China. Journal of Earth Science, 27(4): 686–698. https://doi.org/10.1007/s12583-015-0607-y CrossRefGoogle Scholar
  23. Lion, G. I., Panet, I., Wolf, P., et al., 2017. Determination of a High Spatial Resolution Geopotential Model Using Atomic Clock Comparisons. Journal of Geodesy, 91(6): 597–611. https://doi.org/10.13039/501100000781 CrossRefGoogle Scholar
  24. Lisdat, C., Grosche, G., Quintin, N., et al., 2016. A Clock Network for Geodesy and Fundamental Science. Nature Communications, 7: 12443. https://doi.org/10.1038/ncomms12443 CrossRefGoogle Scholar
  25. Lopez, O., Haboucha, A., Chanteau, B., et al., 2012. Ultra-Stable Long Distance Optical Frequency Distribution Using the Internet Fiber Network. Optics Express, 20(21): 23518. https://doi.org/10.1364/oe.20.023518 CrossRefGoogle Scholar
  26. Lopez, O., Kanj, A., Pottie, P. E., et al., 2013. Simultaneous Remote Transfer of Accurate Timing and Optical Frequency over a Public Fiber Network. Applied Physics B, 110(1): 3–6. https://doi.org/10.1007/s00340-012-5241-0 CrossRefGoogle Scholar
  27. Ludlow, A. D., Zelevinsky, T., Campbell, G. K., et al., 2008. Sr Lattice Clock at 1×10-16 Fractional Uncertainty by Remote Optical Evaluation with a Ca Clock. Science, 319(5871): 1805–1808. https://doi.org/10.1126/science.1153341 CrossRefGoogle Scholar
  28. Ma, L. S., Bartels, A., Robertsson, L., et al., 2004. Optical Frequency Synthesis and Comparison with Uncertainty at the 10–19 Level. Science, 303(5665): 1843–1845. https://doi.org/10.1126/science.1095092 CrossRefGoogle Scholar
  29. Ma, L. S., Jungner, P., Ye, J., et al., 1994. Delivering the Same Optical Frequency at Two Places: Accurate Cancellation of Phase Noise Introduced by an Optical Fiber or other Time-Varying Path. Optics Letters, 19(21): 1777–1779. https://doi.org/10.1364/ol.19.001777 CrossRefGoogle Scholar
  30. Madej, A. A., Dubé, P., Zhou, Z. C., et al., 2012. 88Sr+ 445-THz Single-Ion Reference at the 10–17 Level via Control and Cancellation of Systematic Uncertainties and Its Measurement against the SI Second. Physical Review Letters, 109(20): 203002. https://doi.org/10.1103/physrevlett.109.203002 CrossRefGoogle Scholar
  31. Mai, E., 2013. Time, Atomic Clocks, and Relativistic Geodesy. Deutsche Geodätische Kommission, Reihe A, Theoretische Geodäsie, Heft Nr. 124, Verlag der Bayerischen Akademie der Wissenschaften, MünchenGoogle Scholar
  32. Marra, G., Slavík, R., Margolis, H. S., et al., 2011. High-Resolution Microwave Frequency Transfer over an 86-km-Long Optical Fiber Network Using a Mode-Locked Laser. Optics Letters, 36(4): 511. https://doi.org/10.13039/501100000821 CrossRefGoogle Scholar
  33. Müller, H., Peters, A., Chu, S., 2010. A Precision Measurement of the Gravitational Redshift by the Interference of Matter Waves. Nature, 463(7283): 926–929. https://doi.org/10.1038/nature08776 CrossRefGoogle Scholar
  34. Newbury, N. R., Swann, W. C., Coddington, I., et al., 2007a. Fiber Laser-Based Frequency Combs with High Relative Frequency Stability. Frequency Control Symposium, 2007 Joint with the 21st European Frequency and Time Forum. IEEE International. 980–983. https://doi.org/10.1109/FREQ.2007.4319226 Google Scholar
  35. Newbury, N. R., Williams, P. A., Swann, W. C., 2007b. Coherent Transfer of an Optical Carrier over 251 km. Optics Letters, 32(21): 3056–3058. https://doi.org/10.1364/ol.32.003056 CrossRefGoogle Scholar
  36. Pound, R. V., Rebka, G. A. Jr., 1959. Gravitational Red-Shift in Nuclear Resonance. Physical Review Letters, 3(9): 439–441. https://doi.org/10.1103/physrevlett.3.439 CrossRefGoogle Scholar
  37. Pound, R. V., Rebka, G. A. Jr., 1960a. Attempts to Detect Resonance Scattering InZn67; The Effect of Zero-Point Vibrations. Physical Review Letters, 4(8): 397–399. https://doi.org/10.1103/physrevlett.4.397 CrossRefGoogle Scholar
  38. Pound, R. V., Rebka, G. A. Jr., 1960b. Variation with Temperature of the Energy of Recoil-Free Gamma Rays from Solids. Physical Review Letters, 4(6): 274–275. https://doi.org/10.1103/physrevlett.4.274 CrossRefGoogle Scholar
  39. Pound, R. V., Snider, J. L., 1965. Effect of Gravity on Gamma Radiation. Physical Review, 140(3B): B788–B803. https://doi.org/10.1103/physrev.140.b788 CrossRefGoogle Scholar
  40. Predehl, K., Grosche, G., Raupach, S. M. F., et al., 2012. A 920-Kilometer Optical Fiber Link for Frequency Metrology at the 19th Decimal Place. Science, 336(6080): 441–444. https://doi.org/10.1126/science.1218442 CrossRefGoogle Scholar
  41. Primas, L. E., Lutes, G. F., Sydnor, R. L., 1988. Fiber Optic Frequency Transfer Link. Proceedings of 42nd Annual Symposium on Frequency Control, June 1–3, 1988, Baltimore, MD. 478–484Google Scholar
  42. Raupach, S. M. F., Grosche, G., 2013. Chirped Frequency Transfer with an Accuracy of 10–18 and Its Application to the Remote Synchronization of Timescales. arXiv: 1308.6725v2 [physics.optics] (2013-9-30)Google Scholar
  43. Raupach, S. M. F., Koczwara, A., Grosche, G., 2014. Optical Frequency Transfer via a 660 km Underground Fiber Link Using a Remote Brillouin Amplifier. Optics Express, 22(22): 26537–26547. https://doi.org/10.1364/oe.22.026537 CrossRefGoogle Scholar
  44. Rosenband, T., Hume, D. B., Schmidt, P. O., et al., 2008. Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks, Metrology at the 17th Decimal Place. Science, 319(5871): 1808–1812. https://doi.org/10.1126/science.1154622 CrossRefGoogle Scholar
  45. Shen, W.-B., 1998. Relativistic Physical Geodesy: [Dissertation]. Graz Technical University, GrazGoogle Scholar
  46. Shen, W.-B., 2013a. Orthometric Height Determination Based upon Optical Clocks and Fiber Frequency Transfer Technique. 2013 Saudi International Electronics, Communications and Photonics Conference (SIECPC), April 27–30, 2013, Riyadh, Saudi Arabia. https://doi.org/10.1109/SIECPC.2013.6550987 Google Scholar
  47. Shen, W.-B., 2013b. Orthometric Height Determination Using Optical Clocks. EGU General Assembly Conference Abstracts, 15: 5214Google Scholar
  48. Shen, W.-B., Chao, D., Jin, B., 1993. On Relativistic Geoid. Bollettino di Geodesia e Scienze Affini, 52(3): 207–216Google Scholar
  49. Shen, W.-B., Ning, J. S., Chao, D. B., et al., 2009. A Proposal on the Test of Gen eral Relativity by Clock Transportation Experiments. Advances in Space Research, 43(1): 164–166. https://doi.org/10.1016/j.asr.2008.04.001 CrossRefGoogle Scholar
  50. Shen, W.-B., Ning, J. S., Liu, J. N., et al., 2011. Determination of the Geopotential and Orthometric Height Based on Frequency Shift Equation. Natural Science, 3(5): 388–396. https://doi.org/10.4236/ns.2011.35052 CrossRefGoogle Scholar
  51. Shen, W.-B., Peng, Z., 2012. Gravity Potential Determination Using Remote Optical Fiber. International Symposium on Gravity, Geoid and Height Systems GGHS 2012. Dec. 3, 2012, Venice, ItalyGoogle Scholar
  52. Shen, Z. Y., Shen, W.-B., Zhang, S. X., 2016. Formulation of Geopotential Difference Determination Using Optical-Atomic Clocks Onboard Satellites and on Ground Based on Doppler Cancellation System. Geophysical Journal International, 206(2): 1162–1168. https://doi.org/10.1093/gji/ggw198 CrossRefGoogle Scholar
  53. Shen, Z. Y., Shen, W.-B., Zhang, S. X., 2017. Determination of Gravitational Potential at Ground Using Optical-Atomic Clocks on Board Satellites and on Ground Stations and Relevant Simulation Experiments. Surveys in Geophysics, 38(4): 757–780. https://doi.org/10.1007/s10712-017-9414-6 CrossRefGoogle Scholar
  54. Snider, J. L., 1972. New Measurement of the Solar Gravitational Red Shift. Physical Review Letters, 28(13): 853–856. https://doi.org/10.1103/physrevlett.28.853 CrossRefGoogle Scholar
  55. Soffel, M., Herold, H., Ruder, H., et al., 1988a. Relativistic Geodesy: The Concept of Asymptotically Fixed Reference Frames. Manuscr. Geod., 13(3): 139–142Google Scholar
  56. Soffel, M., Herold, H., Ruder, H., et al., 1988b. Relativistic Theory of Gravimetric Measurements and Definition of the Geoid. Manuscr. Geod., 13: 143–146Google Scholar
  57. Takano, T., Takamoto, M., Ushijima, I., et al., 2016. Geopotential Measurements with Synchronously Linked Optical Lattice Clocks. Nature Photonics, 10(10): 662–666. https://doi.org/10.1038/nphoton.2016.159 CrossRefGoogle Scholar
  58. Tenzer, R., Bagherbandi, M., 2016. Theoretical Deficiencies of Isostatic Schemes in Modeling the Crustal Thickness along the Convergent Continental Tectonic Plate Boundaries. Journal of Earth Science, 27(6): 1045–1053. https://doi.org/10.1007/s12583-015-0608-x CrossRefGoogle Scholar
  59. Turneaure, J. P., Will, C. M., Farrell, B. F., et al., 1983. Test of the Principle of Equivalence by a Null Gravitational Red-Shift Experiment. Physical Review D, 27(8): 1705–1714. https://doi.org/10.1103/physrevd.27.1705 CrossRefGoogle Scholar
  60. Ushijima, I., Takamoto, M., Das, M., et al., 2015. Cryogenic Optical Lattice Clocks. Nature Photonics, 9(3): 185–189. https://doi.org/10.1038/nphoton.2015.5 CrossRefGoogle Scholar
  61. Vessot, R. F. C., Levine, M. W., 1979. A Test of the Equivalence Principle Using a Space-Borne Clock. General Relativity and Gravitation, 10(3): 181–204. https://doi.org/10.1007/bf00759854 CrossRefGoogle Scholar
  62. Vessot, R. F. C., Levine, M. W., Mattison, E. M., et al., 1980. Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser. Physical Review Letters, 45(26): 2081–2084. https://doi.org/10.1103/physrevlett.45.2081 CrossRefGoogle Scholar
  63. Wada, M., Watabe, K.-I., Okubo, S., et al., 2015. A Precise Frequency Comparison System Using an Optical Carrier. Electronics and Communications in Japan, 98: 19–27CrossRefGoogle Scholar
  64. Weinberg, S., 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New YorkGoogle Scholar
  65. Ye, J., Peng, J.-L., Jones, R. J., et al., 2003. Delivery of High-Stability Optical and Microwave Frequency Standards over an Optical Fiber Network. Journal of the Optical Society of America B, 20(7): 1459. https://doi.org/10.1364/josab.20.001459 Google Scholar

Copyright information

© China University of Geosciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Resource and EnvironmentHubei University of Science and TechnologyXianningChina
  2. 2.Time and Frequency Geodesy Research Center, School of Geodesy and Geomatics, Department of Geophysics, Key Laboratory of Geospace Environment and Geodesy of the Ministry of EducationWuhan UniversityWuhanChina
  3. 3.State Key Laboratory of Information Engineering in Surveying, Mapping and Remote SensingWuhan UniversityWuhanChina
  4. 4.National Time Service Center (NTSC)Chinese Academy of SciencesXiʼanChina

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