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Amplification of waves from a rotating body


In 1971, Zel’dovich predicted that quantum fluctuations and classical waves reflected from a rotating absorbing cylinder will gain energy and be amplified. This concept, which is a key step towards the understanding that black holes may amplify quantum fluctuations, has not been verified experimentally owing to the challenging experimental requirement that the cylinder rotation rate must be larger than the incoming wave frequency. Here, we demonstrate experimentally that these conditions can be satisfied with acoustic waves. We show that low-frequency acoustic modes with orbital angular momentum are transmitted through an absorbing rotating disk and amplified by up to 30% or more when the disk rotation rate satisfies the Zel’dovich condition. These experiments address an outstanding problem in fundamental physics and have implications for future research into the extraction of energy from rotating systems.

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Fig. 1: Schematic outline of experiment.
Fig. 2: Spectrally resolved acoustic measurements.
Fig. 3: The effect of rotation.
Fig. 4: Evidence of absolute gain.
Fig. 5: Comparison of different OAM beams.

Data availability

Source data are provided with this paper. All other data used to make the figures in this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Penrose, R. Gravitational collapse: the role of general relativity. Riv. Nuovo Cim. Num. Spez. I, 257–276 (1969).

    Google Scholar 

  2. Zel’dovich, Ya. B. Generation of waves by a rotating body. JETP Lett. 14, 180–181 (1971).

    ADS  Google Scholar 

  3. Zel’dovich, Ya. B. Amplification of cylindrical electromagnetic waves reflected from a rotating body. J. Exp. Theor. Phys. 35, 1085–1087 (1972).

    ADS  Google Scholar 

  4. Zel’dovich, Ya. B., Rozhanskii, L. V. & Starobinskii, A. A. Rotating bodies and electrodynamics in a rotating coordinate system. Radiophys. Quantum Electron. 29, 761–768 (1986).

    Article  ADS  Google Scholar 

  5. Acheson, D. J. On over-reflexion. J. Fluid Mech. 77, 433–472 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  6. Torres, T. et al. Rotational superradiant scattering in a vortex flow. Nat. Phys. 13, 833–836 (2017).

    Article  Google Scholar 

  7. Weinfurtner, S., Tedford, E. W., Penrice, M. C. J., Unruh, W. G. & Lawrence, G. A. Measurement of stimulated Hawking emission in an analogue system. Phys. Rev. Lett. 106, 021302 (2011).

    Article  ADS  Google Scholar 

  8. Belgiorno, F. et al. Hawking radiation from ultrashort laser pulse filaments. Phys. Rev. Lett. 105, 203901 (2010).

    Article  ADS  Google Scholar 

  9. Drori, J., Rosenberg, Y., Bermudez, D., Silberberg, Y. & Leonhardt, U. Observation of stimulated Hawking radiation in an optical analogue. Phys. Rev. Lett. 122, 010404 (2019).

    Article  ADS  Google Scholar 

  10. Steinhauer, J. Observation of self-amplifying Hawking radiation in an analogue black-hole laser. Nat. Phys. 10, 864–869 (2014).

    Article  Google Scholar 

  11. Steinhauer, J. Observation of quantum Hawking radiation and its entanglement in an analogue black hole. Nat. Phys. 12, 959–965 (2016).

    Article  Google Scholar 

  12. Muñoz de Nova, J. R., Golubkov, K., Kolobov, V. I. & Steinhauer, J. Observation of thermal Hawking radiation and its temperature in an analogue black hole. Nature 569, 688–691 (2019).

    Article  ADS  Google Scholar 

  13. Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992).

    Article  ADS  Google Scholar 

  14. Andrews, D. & Babiker, M. The Angular Momentum of Light (Cambridge Univ. Press, 2012).

  15. Padgett, M., Courtial, J. & Allen, L. Light’s orbital angular momentum. Phys. Today 57, 35–40 (2004).

    Article  ADS  Google Scholar 

  16. Fickler, R., Campbell, G., Buchler, B., Lam, P. K. & Zeilinger, A. Quantum entanglement of angular momentum states with quantum numbers up to 10,010. Proc. Natl Acad. Sci. USA 113, 13642–13647 (2016).

    Article  ADS  Google Scholar 

  17. Faccio, D. & Wright, E. M. Nonlinear Zel’dovich effect: parametric amplification from medium rotation. Phys. Rev. Lett. 118, 093901 (2017).

    Article  ADS  Google Scholar 

  18. Gooding, C., Weinfurtner, S. & Unruh, W. G. Reinventing the Zel’dovich wheel. Preprint at (2019).

  19. Faccio, D. & Wright, E. M. Superradiant amplification of acoustic beams via medium rotation. Phys. Rev. Lett. 123, 044301 (2019).

    Article  ADS  Google Scholar 

  20. Gooding, C., Weinfurtner, S. & Unruh, W. G. Superradiant scattering of orbital angular momentum beams. Preprint at (2020).

  21. Gooding, C. Dynamics landscape for acoustic superradiance. Preprint at (2020).

  22. Courtial, J., Robertson, D. A., Dholakia, K., Allen, L. & Padgett, M. J. Rotational frequency shift of a light beam. Phys. Rev. Lett. 81, 4828–4830 (1998).

    Article  ADS  Google Scholar 

  23. Bialynicki-Birula, I. & Bialynicka-Birula, Z. Rotational frequency shift. Phys. Rev. Lett. 78, 2539–2542 (1997).

    Article  ADS  Google Scholar 

  24. Gibson, G. M. et al. Reversal of orbital angular momentum arising from an extreme Doppler shift. Proc. Natl Acad. Sci. USA 115, 3800–3803 (2018).

    Article  ADS  Google Scholar 

  25. Boyd, R. Nonlinear Optics 3rd edn (Academic Press, 2008).

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This work was supported by the UK EPSRC (grant no. EP/P006078/2) and the Horizon 2020 research and innovation programme of the European Union (grant agreement no. 820392).

Author information

Authors and Affiliations



M.C. performed the measurements and data analysis. G.M.G., E.T. and M.C. built the experiment. E.M.W., D.F. and M.J.P. conceived the experiment and theory. All authors contributed to the manuscript.

Corresponding authors

Correspondence to Miles J. Padgett or Daniele Faccio.

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Competing interests

The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Photograph of set-up.

Photograph of the set-up showing the detail of the interaction region where the acoustic waveguides conduct the sound directly on to the absorber, supported by a plastic disk.

Extended Data Fig. 2 Microphone response (with no absorber).

Microphone calibration: measurements of response when both microphones have no absorber placed in front of them, showing that the microphones are both calibrated and measure the same signal, as desired.

Source data

Extended Data Fig. 3 Microphone response (with absorber).

Microphone calibration: measurements of response when both microphones have absorbers placed in front of them, showing that the microphones are both calibrated and measure the same signal, as desired.

Source data

Supplementary information

Supplementary Video 1

Animated video spectrogram, to hear how the measured audio signal varies with rotational frequency. The pitch has been increased to be in the human hearing range.

Source data

Source Data Fig. 2

Numerical matrix for spectrogram.

Source Data Fig. 3

Numerical data points.

Source Data Fig. 4

Numerical data points and error bars.

Source Data Fig. 5

Numerical data points.

Source Data Extended Data Fig. 2

Numerical data points.

Source Data Extended Data Fig. 3

Numerical data points.

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Cromb, M., Gibson, G.M., Toninelli, E. et al. Amplification of waves from a rotating body. Nat. Phys. 16, 1069–1073 (2020).

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