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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.


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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




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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