- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Adaptive robust high-precision atomic gravimetry

Jinye Wei1,2, Jiahao Huang1,2,*, and Chaohong Lee2,3,†

  • *Contact author: hjiahao@mail2.sysu.edu.cn; eqjiahao@gmail. com
  • †Contact author: chleecn@szu.edu.cn; chleecn@gmail.com
PDF

Phys. Rev. Research 7, L012064 – Published 12 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012064

Abstract

Atomic gravimeters are the most accurate sensors for measuring gravity, yet a significant challenge lies in achieving high precision while also maintaining high dynamic range and robustness. Here, we develop a protocol for achieving robust high-precision atomic gravimetry based upon adaptive Bayesian quantum estimation. Our protocol incorporates a sequence of interferometry measurements taken with short to long interrogation times and offers several crucial advantages. Firstly, it enables a high dynamic range without the need to scan multiple fringes for pre-estimation, making it more efficient than the conventional frequentist method. Secondly, it improves robustness against noises, allowing for a significant improvement in measurement precision in noisy environments. The enhancement can be more than 5 times for a transportable gravimeter [Sci. Adv. 5, eaax0800 (2019)] and up to an order of magnitude for a state-of-the-art fountain gravimeter [Phys. Rev. A 88, 043610 (2013)]. Notably, by optimizing the interferometry sequence, our approach can improve the scaling of the measurement precision (Δgest) versus the total interrogation time (T̃) to Δgest∝T̃−2 or even better, in contrast to the conventional one Δgest∝T̃−0.5. Our approach offers superior precision, increased dynamic range, and enhanced robustness, making it highly promising for a range of practical sensing applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (77)

  1. A. Peters, K. Y. Chung, and S. Chu, Measurement of gravitational acceleration by dropping atoms, Nature (London) 400, 849 (1999).
  2. A. Peters, K. Y. Chung, and S. Chu, High-precision gravity measurements using atom interferometry, Metrologia 38, 25 (2001).
  3. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009).
  4. N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter, Phys. Rev. Lett. 106, 038501 (2011).
  5. P. Altin, M. Johnsson, V. Negnevitsky, G. Dennis, R. P. Anderson, J. Debs, S. Szigeti, K. Hardman, S. Bennetts, G. McDonald et al., Precision atomic gravimeter based on Bragg diffraction, New J. Phys. 15, 023009 (2013).
  6. M. Kritsotakis, S. S. Szigeti, J. A. Dunningham, and S. A. Haine, Optimal matter-wave gravimetry, Phys. Rev. A 98, 023629 (2018).
  7. K. Bongs, M. Holynski, J. Vovrosh, P. Bouyer, G. Condon, E. Rasel, C. Schubert, W. P. Schleich, and A. Roura, Taking atom interferometric quantum sensors from the laboratory to real-world applications, Nat. Rev. Phys. 1, 731 (2019).
  8. S. S. Szigeti, S. P. Nolan, J. D. Close, and S. A. Haine, High-precision quantum-enhanced gravimetry with a Bose-Einstein condensate, Phys. Rev. Lett. 125, 100402 (2020).
  9. C.-Y. Li, J.-B. Long, M.-Q. Huang, B. Chen, Y.-M. Yang, X. Jiang, C.-F. Xiang, Z.-L. Ma, D.-Q. He, L.-K. Chen et al., Continuous gravity measurement with a portable atom gravimeter, Phys. Rev. A 108, 032811 (2023).
  10. C. Jekeli, Navigation error analysis of atom interferometer inertial sensor, Navigation 52, 1 (2005).
  11. Y. Han, B. Wang, Z. Deng, and M. Fu, An improved TERCOM-based algorithm for gravity-aided navigation, IEEE Sens. J. 16, 2537 (2016).
  12. P. Cheiney, L. Fouché, S. Templier, F. Napolitano, B. Battelier, P. Bouyer, and B. Barrett, Navigation-compatible hybrid quantum accelerometer using a Kalman filter, Phys. Rev. Appl. 10, 034030 (2018).
  13. H. Zhu, P. Huang, B. Gao, B. Tang, X. Chen, J. Zhong, J. Wang, and M. Zhan, Miniaturized optical system for high-precision mobile atomic gravimeters, Opt. Express 32, 26157 (2024).
  14. A. Lambert, N. Courtier, G. S. Sasagawa, F. Klopping, D. Winester, T. S. James, and J. O. Liard, New constraints on Laurentide postglacial rebound from absolute gravity measurements, Geophys. Res. Lett. 28, 2109 (2001).
  15. J. Park, T.-R. A. Song, J. Tromp, E. Okal, S. Stein, G. Roult, E. Clevede, G. Laske, H. Kanamori, P. Davis et al., Earth's free oscillations excited by the 26 December 2004 Sumatra-Andaman earthquake, Science 308, 1139 (2005).
  16. J.-P. Montagner, K. Juhel, M. Barsuglia, J. P. Ampuero, E. Chassande-Mottin, J. Harms, B. Whiting, P. Bernard, E. Clévédé, and P. Lognonné, Prompt gravity signal induced by the 2011 Tohoku-Oki earthquake, Nat. Commun. 7, 13349 (2016).
  17. J. Chen, C. Wilson, and B. Tapley, Satellite gravity measurements confirm accelerated melting of Greenland ice sheet, Science 313, 1958 (2006).
  18. M. G. Tarallo, T. Mazzoni, N. Poli, D. V. Sutyrin, X. Zhang, and G. M. Tino, Test of Einstein equivalence principle for 0-spin and half-integer-spin atoms: search for spin-gravity coupling effects, Phys. Rev. Lett. 113, 023005 (2014).
  19. G. Rosi, L. Cacciapuoti, F. Sorrentino, M. Menchetti, M. Prevedelli, and G. M. Tino, Measurement of the gravity-field curvature by atom interferometry, Phys. Rev. Lett. 114, 013001 (2015).
  20. T. Kovachy, P. Asenbaum, C. Overstreet, C. A. Donnelly, S. M. Dickerson, A. Sugarbaker, J. M. Hogan, and M. A. Kasevich, Quantum superposition at the half-metre scale, Nature (London) 528, 530 (2015).
  21. X.-C. Duan, X.-B. Deng, M.-K. Zhou, K. Zhang, W.-J. Xu, F. Xiong, Y.-Y. Xu, C.-G. Shao, J. Luo, and Z.-K. Hu, Test of the universality of free fall with atoms in different spin orientations, Phys. Rev. Lett. 117, 023001 (2016).
  22. P. Asenbaum, C. Overstreet, T. Kovachy, D. D. Brown, J. M. Hogan, and M. A. Kasevich, Phase shift in an atom interferometer due to spacetime curvature across its wave function, Phys. Rev. Lett. 118, 183602 (2017).
  23. P. Asenbaum, C. Overstreet, M. Kim, J. Curti, and M. A. Kasevich, Atom-interferometric test of the equivalence principle at the 10- 12 level, Phys. Rev. Lett. 125, 191101 (2020).
  24. P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, New method for gravitational wave detection with atomic sensors, Phys. Rev. Lett. 110, 171102 (2013).
  25. T. Zhang, L.-L. Chen, Y.-B. Shu, W.-J. Xu, Y. Cheng, Q. Luo, Z.-K. Hu, and M.-K. Zhou, Ultrahigh-sensitivity Bragg atom gravimeter and its application in testing Lorentz violation, Phys. Rev. Appl. 20, 014067 (2023).
  26. S. Dimopoulos, P. W. Graham, J. M. Hogan, and M. A. Kasevich, Testing general relativity with atom interferometry, Phys. Rev. Lett. 98, 111102 (2007).
  27. J. Lautier, L. Volodimer, T. Hardin, S. Merlet, M. Lours, F. Pereira Dos Santos, and A. Landragin, Hybridizing matter-wave and classical accelerometers, Appl. Phys. Lett. 105, 144102 (2014).
  28. B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig et al., Quantum tests of the Einstein equivalence principle with the STE–QUEST space mission, Adv. Space Res. 55, 501 (2015).
  29. X. Wu, Z. Pagel, B. S. Malek, T. H. Nguyen, F. Zi, D. S. Scheirer, and H. Müller, Gravity surveys using a mobile atom interferometer, Sci. Adv. 5, eaax0800 (2019).
  30. M. Guo, J. Bai, D. Hu, Z. Tang, J. You, R. Chen, and Y. Wang, A vibration correction system for cold atom gravimeter, Meas. Sci. Technol. 35, 035011 (2024).
  31. C. D. Panda, M. Tao, M. Ceja, A. Reynoso, and H. Müller, Atomic gravimeter robust to environmental effects, Appl. Phys. Lett. 123, 064001 (2023).
  32. B.-N. Jiang, A two-state Kalman estimator for atomic gravimetry, Eur. Phys. J. D 78, 98 (2024).
  33. V. Baryshev and I. Y. Blinov, Application of atomic interferometers in gravimetry, Meas. Tech. 57, 1333 (2015).
  34. O. Carraz, F. Lienhart, R. Charrière, M. Cadoret, N. Zahzam, Y. Bidel, and A. Bresson, Compact and robust laser system for onboard atom interferometry, Appl. Phys. B 97, 405 (2009).
  35. L. Zhou, Z.-Y. Xiong, W. Yang, B. Tang, W.-C. Peng, Y.-B. Wang, P. Xu, J. Wang, and M.-S. Zhan, Measurement of local gravity via a cold atom interferometer, Chinese Phys. Lett. 28, 013701 (2011).
  36. S. Abend, M. Gebbe, M. Gersemann, H. Ahlers, H. Müntinga, E. Giese, N. Gaaloul, C. Schubert, C. Lämmerzahl, W. Ertmer et al., Atom-chip fountain gravimeter, Phys. Rev. Lett. 117, 203003 (2016).
  37. C. Freier, M. Hauth, V. Schkolnik, B. Leykauf, M. Schilling, H. Wziontek, H.-G. Scherneck, J. Müller, and A. Peters, Mobile quantum gravity sensor with unprecedented stability, J. Phys.: Conf. Ser. 723, 012050 (2016).
  38. K. B. Samuel Lellouch and M. Holynski, Using atom interferometry to measure gravity, Contemp. Phys. 63, 138 (2022).
  39. D. W. Berry and H. M. Wiseman, Optimal states and almost optimal adaptive measurements for quantum interferometry, Phys. Rev. Lett. 85, 5098 (2000).
  40. S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O'Brien, and M. G. Thompson, Experimental Bayesian quantum phase estimation on a silicon photonic chip, Phys. Rev. Lett. 118, 100503 (2017).
  41. J. Wang, S. Paesani, R. Santagati, S. Knauer, A. A. Gentile, N. Wiebe, M. Petruzzella, J. L. O'Brien, J. G. Rarity, A. Laing et al., Experimental quantum Hamiltonian learning, Nat. Phys. 13, 551 (2017).
  42. A. Lumino, E. Polino, A. S. Rab, G. Milani, N. Spagnolo, N. Wiebe, and F. Sciarrino, Experimental phase estimation enhanced by machine learning, Phys. Rev. Appl. 10, 044033 (2018).
  43. S. Nolan, A. Smerzi, and L. Pezzè, A machine learning approach to Bayesian parameter estimation, npj Quantum Inf. 7, 169 (2021).
  44. Y. Qiu, M. Zhuang, J. Huang, and C. Lee, Efficient Bayesian phase estimation via entropy-based sampling, Quantum Sci. Technol. 7, 035022 (2022).
  45. J. K. Stockton, X. Wu, and M. A. Kasevich, Bayesian estimation of differential interferometer phase, Phys. Rev. A 76, 033613 (2007).
  46. V. Gebhart, R. Santagati, A. A. Gentile, E. M. Gauger, D. Craig, N. Ares, L. Banchi, F. Marquardt, L. Pezzè, and C. Bonato, Learning quantum systems, Nat. Rev. Phys. 5, 141 (2023).
  47. T. Ruster, H. Kaufmann, M. A. Luda, V. Kaushal, C. T. Schmiegelow, F. Schmidt-Kaler, and U. G. Poschinger, Entanglement-based dc magnetometry with separated ions, Phys. Rev. X 7, 031050 (2017).
  48. R. Santagati, A. A. Gentile, S. Knauer, S. Schmitt, S. Paesani, C. Granade, N. Wiebe, C. Osterkamp, L. P. McGuinness, J. Wang et al., Magnetic-field learning using a single electronic spin in diamond with one-photon readout at room temperature, Phys. Rev. X 9, 021019 (2019).
  49. R. Puebla, Y. Ban, J. F. Haase, M. B. Plenio, M. Paternostro, and J. Casanova, Versatile atomic magnetometry assisted by Bayesian inference, Phys. Rev. Appl. 16, 024044 (2021).
  50. N. Nusran, M. U. Momeen, and M. G. Dutt, High-dynamic-range magnetometry with a single electronic spin in diamond, Nat. Nanotechnol. 7, 109 (2012).
  51. C. Bonato, M. S. Blok, H. T. Dinani, D. W. Berry, M. L. Markham, D. J. Twitchen, and R. Hanson, Optimized quantum sensing with a single electron spin using real-time adaptive measurements, Nat. Nanotechnol. 11, 247 (2016).
  52. E. Turner, S.-H. Wu, X. Li, and H. Wang, Spin-based continuous Bayesian magnetic-field estimations aided by feedback control, Phys. Rev. A 106, 052603 (2022).
  53. K. Craigie, E. M. Gauger, Y. Altmann, and C. Bonato, Resource-efficient adaptive Bayesian tracking of magnetic fields with a quantum sensor, J. Phys.: Condens. Matter 33, 195801 (2021).
  54. C. Han, Z. Ma, Y. Qiu, R. Fang, J. Wu, C. Zhan, M. Li, J. Huang, B. Lu, and C. Lee, Atomic clock locking with Bayesian quantum parameter estimation: Scheme and experiment, Phys. Rev. Appl. 22, 044058 (2024).
  55. A. Cao, W. J. Eckner, T. L. Yelin, A. W. Young, S. Jandura, L. Yan, K. Kim, G. Pupillo, J. Ye, N. D. Oppong, and A. M. Kaufman, Multi-qubit gates and Schrödinger cat states in an optical clock, Nature (London) 634, 315 (2024).
  56. R. S. Said, D. W. Berry, and J. Twamley, Nanoscale magnetometry using a single-spin system in diamond, Phys. Rev. B 83, 125410 (2011).
  57. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, Entanglement-free Heisenberg-limited phase estimation, Nature (London) 450, 393 (2007).
  58. N. Wiebe and C. Granade, Efficient Bayesian phase estimation, Phys. Rev. Lett. 117, 010503 (2016).
  59. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  60. H. T. Dinani, D. W. Berry, R. Gonzalez, J. R. Maze, and C. Bonato, Bayesian estimation for quantum sensing in the absence of single-shot detection, Phys. Rev. B 99, 125413 (2019).
  61. P. Cappellaro, Spin-bath narrowing with adaptive parameter estimation, Phys. Rev. A 85, 030301(R) (2012).
  62. V. Cimini, E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino, Benchmarking Bayesian quantum estimation, Quantum Sci. Technol. 9, 035035 (2024).
  63. D. W. Berry and H. M. Wiseman, Adaptive quantum measurements of a continuously varying phase, Phys. Rev. A 65, 043803 (2002).
  64. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty, and H. Mabuchi, Adaptive homodyne measurement of optical phase, Phys. Rev. Lett. 89, 133602 (2002).
  65. C. Han, J. Huang, X. Jiang, R. Fang, Y. Qiu, B. Lu, and C. Lee, Adaptive Bayesian algorithm for achieving a desired magneto-sensitive transition, Opt. Express 29, 21031 (2021).
  66. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012064 for details on: (i) Principle of an atomic gravimeter; (ii) Procedure of Bayesian gravity estimation; (iii) Calculation of likelihood function; (iv) Point identification method; (v) Derivation of gravity precision scaling with different time sequences; (vi) Influence of contrast on phase estimation precision; (vii) Influence of atom number on measurement precision; (viii) Precision improvement of BGE for other atomic gravimeters.
  67. G. Waldherr, J. Beck, P. Neumann, R. Said, M. Nitsche, M. Markham, D. Twitchen, J. Twamley, F. Jelezko, and J. Wrachtrup, High-dynamic-range magnetometry with a single nuclear spin in diamond, Nat. Nanotechnol. 7, 105 (2012).
  68. J. G. Smith, C. H. W. Barnes, and D. R. M. Arvidsson-Shukur, Adaptive Bayesian quantum algorithm for phase estimation, Phys. Rev. A 109, 042412 (2024).
  69. Z.-K. Hu, B.-L. Sun, X.-C. Duan, M.-K. Zhou, L.-L. Chen, S. Zhan, Q.-Z. Zhang, and J. Luo, Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter, Phys. Rev. A 88, 043610 (2013).
  70. K. Rambhatla, S. E. D'Aurelio, M. Valeri, E. Polino, N. Spagnolo, and F. Sciarrino, Adaptive phase estimation through a genetic algorithm, Phys. Rev. Res. 2, 033078 (2020).
  71. H. Müller, S.-W. Chiow, S. Herrmann, S. Chu, and K.-Y. Chung, Atom-interferometry tests of the isotropy of post-Newtonian gravity, Phys. Rev. Lett. 100, 031101 (2008).
  72. K.-Y. Chung, S.-W. Chiow, S. Herrmann, S. Chu, and H. Müller, Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics, Phys. Rev. D 80, 016002 (2009).
  73. Y. Bidel, N. Zahzam, C. Blanchard, A. Bonnin, M. Cadoret, A. Bresson, D. Rouxel, and M. Lequentrec-Lalancette, Absolute marine gravimetry with matter-wave interferometry, Nat. Commun. 9, 627 (2018).
  74. J.-Y. Zhang, L.-L. Chen, Y. Cheng, Q. Luo, Y.-B. Shu, X.-C. Duan, M.-K. Zhou, and Z.-K. Hu, Movable precision gravimeters based on cold atom interferometry, Chin. Phys. B 29, 093702 (2020).
  75. Y.-Y. Xu, J.-F. Cui, K. Qi, L.-L. Chen, X.-B. Deng, Q. Luo, H. Zhang, Y.-J. Tan, C.-G. Shao, M.-K. Zhou, X.-C. Duan, and Z.-K. Hu, Evaluation of the transportable atom gravimeter HUST-QG, Metrologia 59, 055001 (2022).
  76. J. Zhong, B. Tang, X. Chen, and L. Zhou, Quantum gravimetry going toward real applications, The Innovation 3, 100230 (2022).
  77. J. Chen, Analysis of the principle and state-of-art facilities of mobile atom interferometry gravity, Highl. Sci. Eng. Technol. 72, 511 (2023).

Outline

Information

Phys. Rev. Research 7, L012064– Published 12 March, 2025
  • Received 29 August 2024
  • Accepted 26 February 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation