A Gravitational Aharonov-Bohm Effect, and Its Connection to Parametric Oscillators and Gravitational Radiation

  • Raymond Y. ChiaoEmail author
  • Robert W. Haun
  • Nader A. Inan
  • Bong-Soo Kang
  • Luis A. Martinez
  • Stephen J. Minter
  • Gerardo A. Munoz
  • Douglas A. Singleton
Conference paper


A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. We begin the analysis starting from four Maxwell-like equations for weak gravitational fields interacting with slowly moving matter. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, and applied to the problem of the interaction of radiation with macroscopically coherent quantum systems, including the problem of gravitational radiation interacting with superconductors. But first we examine the interaction of EM radiation with superconductors in a parametric oscillator consisting of a superconducting wire placed at the center of a high Q superconducting cavity driven by pump microwaves. Some room-temperature data will be presented demonstrating the splitting of a single microwave cavity resonance into a spectral doublet due to the insertion of a central wire. This would represent an unseparated kind of parametric oscillator, in which the signal and idler waves would occupy the same volume of space. We then propose a separated parametric oscillator experiment, in which the signal and idler waves are generated in two disjoint regions of space, which are separated from each other by means of an impermeable superconducting membrane. We find that the threshold for parametric oscillation for EM microwave generation is much lower for the separated configuration than the unseparated one, which then leads to an observable dynamical Casimir effect. We speculate that a separated parametric oscillator for generating coherent GR microwaves could also be built. [Editor’s note: for a video of the talk given by Prof. Chiao at the Aharonov-80 conference in 2012 at Chapman University, see]


Parametric Oscillator Pump Wave Stokes Wave Transverse Magnetic Mode Idle Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



D.A.S. acknowledges the support of a 2012–2013 Fulbright Senior Scholar Grant. We thank Jay Sharping for his help in our experiments.


  1. 1.
    M.A. Hohensee, B. Estey, P. Hamilton, A. Zeilinger, H. Müller, Force-free gravitational redshift: proposed gravitational Aharonov-Bohm experiment. Phys. Rev. Lett. 108, 230404 (2012). Here we consider a thought experiment to see the vector gravitational AB effect instead of the scalar gravitational AB effect. ADSCrossRefGoogle Scholar
  2. 2.
    Y. Aharonov, G. Carmi, Quantum aspects of the equivalence principle. Found. Phys. 3, 493 (1973) ADSCrossRefGoogle Scholar
  3. 3.
    E.G. Harris, The gravitational Aharonov-Bohm effect with photons. Am. J. Phys. 64, 378 (1996). Here we consider the AB effect with electrons rather than photons. The AB effect with photons could be understood entirely classically in terms of classical EM waves diffracting around a “solenoid.” However, no such classical explanation would exist for the electron interference experiment described in Fig. 14.1 ADSCrossRefGoogle Scholar
  4. 4.
    J.M. Cohen, B. Mashhoon, Standard clocks, interferometry, and gravitomagnetism. Phys. Lett. A 181, 353 (1993) ADSCrossRefGoogle Scholar
  5. 5.
    A. Tartaglia, Gravitational Aharonov-Bohm effect and gravitational lensing. gr-qc/0003030
  6. 6.
    R. Owen et al., Frame-dragging vortexes and tidal tendexes attached to colliding black holes: visualizing the curvature of spacetime. Phys. Rev. Lett. 106, 151101 (2011). arXiv:1012.4869 MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    D.A. Nichols et al., Visualizing spacetime curvature via frame-drag vortexes and tidal tendexes: general theory and weak-gravity applications. Phys. Rev. D 84, 124014 (2011). arXiv:1108.5486 ADSCrossRefGoogle Scholar
  8. 8.
    A. Zimmerman, D.A. Nichols, F. Zhang, Classifying the isolated zeros of asymptotic gravitational radiation by tendex and vortex lines. Phys. Rev. D 84, 044037 (2011). arXiv:1107.2959 ADSCrossRefGoogle Scholar
  9. 9.
    R.H. Price, J.W. Belcher, D.A. Nichols, Comparison of electromagnetic and gravitational radiation; what we can learn about each from the other. arXiv:1212.4730
  10. 10.
    M. Thorsbud, Post-Newtonian methods and the gravito-electromagnetic analogy. Master’s Thesis, Department of Physics, University of Oslo (2010), p. 56 Google Scholar
  11. 11.
    V.B. Braginsky, C.M. Caves, K.S. Thorne, Laboratory experiments to test relativistic gravity. Phys. Rev. D 15, 2047 (1977) ADSCrossRefGoogle Scholar
  12. 12.
    R.L. Forward, General relativity for the experimentalist. Proc. IRE 49, 892 (1961) MathSciNetCrossRefGoogle Scholar
  13. 13.
    A. Tartaglia, M.L. Ruggiero, Gravito-electromagnetism versus electromagnetism. Eur. J. Phys. 25, 203 (2004) CrossRefzbMATHGoogle Scholar
  14. 14.
    Section 4.4 in [18] Google Scholar
  15. 15.
    M. Agop, C.Gh. Buzea, P. Nica, Local gravitoelectromagnetic effects on a superconductor. Physica C 339, 130 (2000) ADSCrossRefGoogle Scholar
  16. 16.
    B. Mashhoon, F. Gronwald, H. Lichtenegger, Gravitomagnetism and the clock effect. Lect. Notes Phys. 562, 83 (2001) ADSCrossRefGoogle Scholar
  17. 17.
    A. Tartaglia, M.L. Ruggiero, Gravitoelectromagnetism versus electromagnetism. Eur. J. Phys. 25, 203 (2004), and Sect. 4.4 of [18] CrossRefzbMATHGoogle Scholar
  18. 18.
    R.M. Wald, General Relativity (University of Chicago Press, Chicago, 1984) CrossRefzbMATHGoogle Scholar
  19. 19.
    H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950). (The meaning of the arrow in “ab” is that “a is to be replaced by b in all the following equations.”) Google Scholar
  20. 20.
    B.S. In, DeWitt’s paper, “Superconductors and gravitational drag”. Phys. Rev. Lett. 16, 1092 (1966), the minimal coupling rule (14.20) was derived from the principle of general covariance which is behind all metric theories of gravity. This principle was applied to a classical, relativistic, spinless point particle, with the rule (14.20) emerging in the limit of low velocities and weak fields CrossRefGoogle Scholar
  21. 21.
    G. Papini, A test of general relativity by means of superconductors. Phys. Lett. 23, 418 (1966) ADSCrossRefGoogle Scholar
  22. 22.
    G. Papini, Detection of inertial effects using superconducting interferometers. Phys. Lett. 24A, 32 (1967) ADSCrossRefGoogle Scholar
  23. 23.
    L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, 4th edn., vol. 2 (Butterworth-Heinemann, Stoneham, 2000) Google Scholar
  24. 24.
    M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A 392, 45 (1984) ADSCrossRefzbMATHGoogle Scholar
  25. 25.
    S.B. Felch, J. Tate, B. Cabrera, J.T. Anderson, Precise determination of h/m e using a rotating, superconducting ring. Phys. Rev. B 31, 7006 (1985). There remain some small, unexplained discrepancies for the inferred electron mass, which are probably due to some unknown systematic errors in the experiment. ADSCrossRefGoogle Scholar
  26. 26.
    M.D. Semon, Experimental verification of an Aharonov-Bohm effect in rotating reference frames. Found. Phys. 7, 49 (1982) MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    R.Y. Chiao, New directions for gravitational-wave physics via ‘Millikan oil drops’, in Visions of Discovery, ed. by R.Y. Chiao, M.L. Cohen, A.J. Leggett, W.D. Phillips, C.L. Harper Jr. (Cambridge University Press, London, 2011), p. 348 Google Scholar
  28. 28.
    J.C. Garrison, R.Y. Chiao, Quantum Optics (Oxford University Press, Oxford, 2008). Equation (2.103) CrossRefGoogle Scholar
  29. 29.
    J.C. Garrison, R.Y. Chiao, Quantum Optics (Oxford University Press, Oxford, 2008). Equation (15.30) CrossRefGoogle Scholar
  30. 30.
    M. Aspelmeyer, P. Meystre, K. Schwab, Quantum optomechanics. Phys. Today 65, 29 (2012) CrossRefGoogle Scholar
  31. 31.
    S. Kuhr, S. Gleyzes, C. Guerlin, J. Bernu, U.B. Hoff, S. Deléglise, S. Osnaghi, M. Brune, J.M. Raimond, S. Haroche, E. Jacques, P. Bosland, B. Visentin, Ultrahigh finesse Fabry-Perot superconducting resonator. Appl. Phys. Lett. 90, 164101 (2007) ADSCrossRefGoogle Scholar
  32. 32.
    R.W. Boyd, Nonlinear Optics (Academic Press, San Diego, 2003) Google Scholar
  33. 33.
    R.Y. Chiao, L.A. Martinez, S.J. Minter, A. Trubarov, Parametric oscillation of a moving mirror driven by radiation pressure in a superconducting Fabry–Perot resonator system. Phys. Scr. T 151, 014073 (2012). arXiv:1207.6885 ADSCrossRefGoogle Scholar
  34. 34.
    M. Philipp, P. von Brentano, G. Pascovici, A. Richter, Frequency and width crossing of two interacting resonances in a microwave cavity. Phys. Rev. E 62, 1922 (2000) ADSCrossRefGoogle Scholar
  35. 35.
    I.G. Wilson, C.W. Schramm, J.P. Kinzer, High Q resonant cavities for microwave testing. Bell Syst. Tech. J. 25(3), 408–434 (1946) CrossRefGoogle Scholar
  36. 36.
    D.J. Griffiths, Introduction to Electrodynamics, 3rd edn. (Prentice Hall, New York, 1999), p. 351 Google Scholar
  37. 37.
    J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998), p. 261 Google Scholar
  38. 38.
    V.B. Braginsky, S.E. Strigin, S.P. Vyatchanin, Parametric oscillatory instability in Fabry-Perot interferometer. Phys. Lett. A 287, 331 (2001) ADSCrossRefGoogle Scholar
  39. 39.
    R.Y. Chiao, Analysis and estimation of the threshold for a microwave ‘pellicle mirror’ parametric oscillator, via energy conservation. arXiv:1211.3519
  40. 40.
    J.C. Garrison, R.Y. Chiao, Quantum Optics (Oxford University Press, Oxford, 2008), p. 89 CrossRefGoogle Scholar
  41. 41.
    P.D. Nation, J.R. Johansson, M.P. Blencowe, F. Nori, Colloquium: stimulating uncertainty: amplifying the quantum vacuum with superconducting circuits. Rev. Mod. Phys. 84, 1 (2012) ADSCrossRefGoogle Scholar
  42. 42.
    S.J. Minter, K. Wegter-McNelly, R.Y. Chiao, Do mirrors for gravitational waves exist? Physica E 42, 234 (2010). arXiv:0903.0661 ADSCrossRefGoogle Scholar
  43. 43.
    C.N. Yang, Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors. Rev. Mod. Phys. 34, 694 (1962) ADSCrossRefGoogle Scholar
  44. 44.
    C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman, San Francisco, 1972) Google Scholar

Copyright information

© Springer-Verlag Italia 2014

Authors and Affiliations

  • Raymond Y. Chiao
    • 1
    Email author
  • Robert W. Haun
    • 2
  • Nader A. Inan
    • 2
  • Bong-Soo Kang
    • 2
  • Luis A. Martinez
    • 2
  • Stephen J. Minter
    • 3
  • Gerardo A. Munoz
    • 4
  • Douglas A. Singleton
    • 5
  1. 1.Schools of Natural Sciences and EngineeringUniversity of California, MercedMercedUSA
  2. 2.School of Natural SciencesUniversity of California, MercedMercedUSA
  3. 3.Vienna Center for Quantum Science and Technology, Faculty of PhysicsUniversity of ViennaViennaAustria
  4. 4.California State University, FresnoFresnoUSA
  5. 5.Department of PhysicsInstitut Teknologi BandungBandungIndonesia

Personalised recommendations