Precision measurement of the Newtonian gravitational constant using cold atoms

Abstract

About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely1. The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G while keeping systematic effects under control. Most previous experiments performed were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish2 in 1798, and in all cases macroscopic masses were used. Here we report the precise determination of G using laser-cooled atoms and quantum interferometry. We obtain the value G = 6.67191(99) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Our value differs by 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology3. A conceptually different experiment such as ours helps to identify the systematic errors that have proved elusive in previous experiments, thus improving the confidence in the value of G. There is no definitive relationship between G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know G has not only a pure metrological interest, but is also important because of the key role that G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models.

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Figure 1: Sketch of the experiment.
Figure 2: Experimental data.
Figure 3: Comparison with previous results.

References

  1. 1

    Quinn, T. Measuring big G. Nature 408, 919–921 (2000)

    CAS  PubMed  Article  ADS  Google Scholar 

  2. 2

    Cavendish, H. Experiments to determine the density of the Earth. Phil. Trans. R. Soc. Lond. 88, 469–526 (1798)

    Article  Google Scholar 

  3. 3

    Mohr, P. J., Taylor, B. N. & Newell, D. B. CODATA recommended values of the fundamental physical constants: 2010. Rev. Mod. Phys. 84, 1527–1605 (2012)

    CAS  Article  ADS  Google Scholar 

  4. 4

    Cronin, A. D., Schmiedmayer, J. & Pritchard, D. E. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009)

    CAS  Article  ADS  Google Scholar 

  5. 5

    Tino G. M., Kasevich M. A., eds. Atom Interferometry, Proc. Int. School Phys. “Enrico Fermi”, Course CLXXXVIII, Varenna 2013 (Società Italiana di Fisica and IOS Press, 2014)

  6. 6

    Peters, A., Chung, K. Y. & Chu, S. Measurement of gravitational acceleration by dropping atoms. Nature 400, 849–852 (1999)

    CAS  Article  ADS  Google Scholar 

  7. 7

    McGuirk, J. M., Foster, G. T., Fixler, J. B., Snadden, M. J. & Kasevich, M. A. Sensitive absolute-gravity gradiometry using atom interferometry. Phys. Rev. A 65, 033608 (2002)

    Article  ADS  CAS  Google Scholar 

  8. 8

    Gustavson, T. L., Landragin, A. & Kasevich, M. A. Rotation sensing with a dual atom interferometer Sagnac gyroscope. Class. Quantum Gravity 17, 2385–2398 (2000)

    CAS  Article  ADS  MATH  Google Scholar 

  9. 9

    Ferrari, G., Poli, N., Sorrentino, F. & Tino, G. M. Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale. Phys. Rev. Lett. 97, 060402 (2006)

    CAS  PubMed  Article  ADS  Google Scholar 

  10. 10

    Dimopoulos, S., Graham, P., Hogan, J. & Kasevich, M. Testing general relativity with atom interferometry. Phys. Rev. Lett. 98, 111102 (2007)

    PubMed  Article  ADS  CAS  Google Scholar 

  11. 11

    Amelino-Camelia, G., Lämmerzahl, C., Mercati, F. & Tino, G. M. Constraining the energy-momentum dispersion relation with Planck-scale sensitivity using cold atoms. Phys. Rev. Lett. 103, 171302 (2009)

    PubMed  Article  ADS  CAS  Google Scholar 

  12. 12

    de Angelis, M. et al. Precision gravimetry with atomic sensors. Meas. Sci. Technol. 20, 022001 (2009)

    Article  CAS  Google Scholar 

  13. 13

    Bertoldi, A. et al. Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G. Eur. Phys. J. D 40, 271–279 (2006)

    CAS  Article  ADS  Google Scholar 

  14. 14

    Fixler, J. B., Foster, G. T., McGuirk, J. M. & Kasevich, M. Atom interferometer measurement of the Newtonian constant of gravity. Science 315, 74–77 (2007)

    CAS  PubMed  Article  ADS  Google Scholar 

  15. 15

    Lamporesi, G., Bertoldi, A., Cacciapuoti, L., Prevedelli, M. & Tino, G. M. Determination of the Newtonian gravitational constant using atom interferometry. Phys. Rev. Lett. 100, 050801 (2008)

    CAS  PubMed  Article  ADS  Google Scholar 

  16. 16

    Tino, G. M. et al. Precision gravity tests with atom interferometry in space. Nucl. Phys. B Proc. Suppl. 243–244 203–217 (2013)

    Article  ADS  CAS  Google Scholar 

  17. 17

    Tino, G. M., Vetrano, F. & Lämmerzahl, C. Editorial on the special issue on “gravitational waves detection with atom interferometry”. Gen. Relativ. Gravit. 43, 1901–1903 (2011)

    MathSciNet  Article  ADS  Google Scholar 

  18. 18

    Louchet-Chauvet, A. et al. The influence of transverse motion within an atomic gravimeter. New J. Phys. 13, 065025 (2011)

    Article  ADS  Google Scholar 

  19. 19

    Kasevich, M. & Chu, S. Atomic interferometry using stimulated Raman transitions. Phys. Rev. Lett. 67, 181–184 (1991)

    CAS  PubMed  Article  ADS  Google Scholar 

  20. 20

    Lamporesi, G. et al. Source masses and positioning system for an accurate measurement of G. Rev. Sci. Instrum. 78, 075109 (2007)

    CAS  PubMed  Article  ADS  Google Scholar 

  21. 21

    Sorrentino, F. et al. Sensitive gravity-gradiometry with atom interferometry: progress towards an improved determination of the gravitational constant. New J. Phys. 12, 095009 (2010)

    Article  ADS  Google Scholar 

  22. 22

    Foster, G. T., Fixler, J. B., McGuirk, J. M. & Kasevich, M. A. novel method of phase extraction between coupled atom interferometers using ellipse-specific fitting. Opt. Lett. 27, 951–953 (2002)

    CAS  PubMed  Article  ADS  Google Scholar 

  23. 23

    Hogan, J., Johnson, D. & Kasevich, M. in Proc. Int. School Phys. “Enrico Fermi”, Course CLXVIII (eds Arimondo, E., Ertmer, W., Schleich, W. & Rasel, E. ) 411–447 (SIF, Bologna and IOS Press, 2009)

    Google Scholar 

  24. 24

    Lan, S.-Y., Kuan, P.-C., Estey, B., Haslinger, P. & Müller, H. Influence of the Coriolis force in atom interferometry. Phys. Rev. Lett. 108, 090402 (2012)

    PubMed  Article  ADS  CAS  Google Scholar 

  25. 25

    Stellmer, S., Pasquiou, B., Grimm, R. & Schreck, F. Laser cooling to quantum degeneracy. Phys. Rev. Lett. 110, 263003 (2013)

    PubMed  Article  ADS  CAS  Google Scholar 

  26. 26

    Sorrentino, F. et al. Quantum sensor for atom-surface interactions below 10 µm. Phys. Rev. A 79, 013409 (2009)

    Article  ADS  CAS  Google Scholar 

  27. 27

    Poli, N. et al. Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter. Phys. Rev. Lett. 106, 038501 (2011)

    CAS  PubMed  Article  ADS  Google Scholar 

  28. 28

    Sorrentino, F. et al. Sensitivity limits of a Raman atom interferometer as a gravity gradiometer. Phys. Rev. A 89, 023607 (2014)

    Article  ADS  CAS  Google Scholar 

  29. 29

    Storey, P. & Cohen-Tannoudji, C. The Feynman path integral approach to atomic interferometry. A tutorial. J. Phys. II France 4, 1999–2027 (1994)

    CAS  Article  Google Scholar 

  30. 30

    Antoine, C. & Bordé, C. Exact phase shifts for atom interferometry. Phys. Lett. A 306, 277–284 (2003)

    CAS  Article  ADS  Google Scholar 

  31. 31

    Luther, G. G. & Towler, W. R. Redetermination of the Newtonian gravitational constant G. Phys. Rev. Lett. 48, 121–123 (1982)

    Article  ADS  Google Scholar 

  32. 32

    Karagioz, O. & Izmailov, V. Measurement of the gravitational constant with a torsion balance. Meas. Tech. 39, 979–987 (1996)

    Article  Google Scholar 

  33. 33

    Bagley, C. H. & Luther, G. G. Preliminary results of a determination of the Newtonian constant of gravitation: a test of the Kuroda hypothesis. Phys. Rev. Lett. 78, 3047–3050 (1997)

    CAS  Article  ADS  Google Scholar 

  34. 34

    Gundlach, J. H. & Merkowitz, S. M. Measurement of Newton’s constant using a torsion balance with angular acceleration feedback. Phys. Rev. Lett. 85, 2869–2872 (2000)

    CAS  PubMed  Article  ADS  Google Scholar 

  35. 35

    Quinn, T. J., Speake, C. C., Richman, S. J., Davis, R. S. & Picard, A. A new determination of G using two methods. Phys. Rev. Lett. 87, 111101 (2001)

    CAS  PubMed  Article  ADS  Google Scholar 

  36. 36

    Kleinevoss, U. Bestimmung der Newtonschen Gravitationskonstanten G. PhD thesis, Univ. Wuppertal. (2002)

  37. 37

    Armstrong, T. R. & Fitzgerald, M. P. New measurements of G using the measurement standards laboratory torsion balance. Phys. Rev. Lett. 91, 201101 (2003)

    CAS  PubMed  Article  ADS  Google Scholar 

  38. 38

    Hu, Z.-K., Guo, J.-Q. & Luo, J. Correction of source mass effects in the HUST-99 measurement of G. Phys. Rev. D 71, 127505 (2005)

    Article  ADS  CAS  Google Scholar 

  39. 39

    Schlamminger, S. et al. Measurement of Newton’s gravitational constant. Phys. Rev. D 74, 082001 (2006)

    Article  ADS  CAS  Google Scholar 

  40. 40

    Luo, J. et al. Determination of the Newtonian gravitational constant G with time-of-swing method. Phys. Rev. Lett. 102, 240801 (2009)

    PubMed  Article  ADS  CAS  MATH  Google Scholar 

  41. 41

    Tu, L.-C. et al. New determination of the gravitational constant G with time-of-swing method. Phys. Rev. D 82, 022001 (2010)

    Article  ADS  CAS  Google Scholar 

  42. 42

    Parks, H. V. & Faller, J. E. Simple pendulum determination of the gravitational constant. Phys. Rev. Lett. 105, 110801 (2010)

    PubMed  Article  ADS  CAS  Google Scholar 

  43. 43

    Quinn, T., Parks, H., Speake, C. & Davis, R. Improved determination of G using two methods. Phys. Rev. Lett. 111, 101102 (2013

    PubMed  Article  ADS  CAS  Google Scholar 

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Acknowledgements

G.M.T. acknowledges discussions with M. A. Kasevich and J. Faller and useful suggestions by A. Peters in the initial phase of the experiment. We are grateful to A. Cecchetti and B. Dulach for the design of the source mass support and to A. Peuto, A. Malengo, and S. Pettorruso for density tests on the tungsten masses. We thank D. Wiersma for a critical reading of the manuscript. This work was supported by INFN (MAGIA experiment).

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G.M.T. had the idea for the experiment, supervised it and wrote the manuscript. G.R., F.S. and L.C. performed the experiment. M.P. contributed to the experiment and analysed the data.

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Correspondence to G. M. Tino.

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The authors declare no competing financial interests.

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Rosi, G., Sorrentino, F., Cacciapuoti, L. et al. Precision measurement of the Newtonian gravitational constant using cold atoms. Nature 510, 518–521 (2014). https://doi.org/10.1038/nature13433

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