Formulation of Determining the Gravity Potential Difference Using Ultra-High Precise Clocks via Optical Fiber Frequency Transfer Technique
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 Wordsgravity frequency shift optical fiber frequency transfer optical clock gravity potential
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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.
- Heiskanen, W. A., Moritz, H., 1967. Physical Geodesy. Freeman and Company, San Francisco Google Scholar
- Hofmann-Wellenhof, B., Moritz, H., 2006. Physical Geodesy. Springer Google Scholar
- 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
- 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
- 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
- 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
- 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
- Shen, W.-B., 1998. Relativistic Physical Geodesy: [Dissertation]. Graz Technical University, GrazGoogle Scholar
- 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
- Shen, W.-B., 2013b. Orthometric Height Determination Using Optical Clocks. EGU General Assembly Conference Abstracts, 15: 5214Google Scholar
- Shen, W.-B., Chao, D., Jin, B., 1993. On Relativistic Geoid. Bollettino di Geodesia e Scienze Affini, 52(3): 207–216Google Scholar
- 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
- 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
- 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
- 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
- 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
- Weinberg, S., 1972. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New YorkGoogle Scholar