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Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole

Abstract

The emission of Hawking radiation from a black hole was predicted to be stationary, which is necessary for the correspondence between Hawking radiation and blackbody radiation. Spontaneous Hawking radiation was observed in analogue black holes in atomic Bose–Einstein condensates, although the stationarity was not probed. Here we confirm that the spontaneous Hawking radiation is stationary by observing such a system at six different times. Furthermore, we follow the time evolution of Hawking radiation and compare and contrast it with predictions for real black holes. We observe the ramp-up of Hawking radiation followed by stationary spontaneous emission, similar to a real black hole. The end of the spontaneous Hawking radiation is marked by the formation of an inner horizon, which is seen to cause stimulated Hawking radiation, as predicted. We find that the stimulated Hawking and partner particles are directly observable, and that the stimulated emission evolves from multi-mode to monochromatic. Numerical simulations suggest that Bogoliubov–Cherenkov–Landau stimulation predominates, rather than black-hole lasing.

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Fig. 1: Spontaneous versus stimulated Hawking radiation.
Fig. 2: The observation of Hawking radiation at various times.
Fig. 3: The evolution of the Hawking radiation.
Fig. 4: The spontaneous and monochromatic periods.
Fig. 5: Numerical simulation of the experiment.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper, and other findings of this study, are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank R. Parentani, N. Pavloff, A. Ori, G. Volovik, T. Jacobson, I. Carusotto and F. Sols for helpful discussions. This work was supported by the Israel Science Foundation.

Author information

Affiliations

Authors

Contributions

J.R.M.d.N. and J.S. designed and built the experimental apparatus. J.R.M.d.N., K.G. and V.I.K. performed theoretical calculations. J.S. acquired the data. K.G., V.I.K. and J.S. analysed the data. J.R.M.d.N. performed the numerical simulations. J.R.M.d.N. and J.S. prepared the manuscript with input from all authors.

Corresponding author

Correspondence to Jeff Steinhauer.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Giovanni Modugno and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Extended data

Extended Data Fig. 1 The structure of the analogue black hole at various times.

The horizon frame is shown. The horizon is at x=0. a, The average external potential U(x). The Bose-Einstein condensate is initially in the minimum A. vup is the applied velocity. b, Ensemble-average density profiles n(x). Time increases from lighter gray to darker gray. The circles indicate the estimated position of the inner horizon. c, The profiles v(x) (black curve) and c(x) (gray curve) which determine the metric. d, Single modes from the preliminary oscillating horizon experiment. G(2)(x,x′) for 30 Hz is shown. The times are the same as in Fig. 2. The grayscale is the same for all plots except the last. The green line indicates the angle determined by the propagation speeds outside (c-v) and inside (v-c) the analogue black hole. e, The time dependence of v (open circles) and c (filled circles) outside the analogue black hole (blue) and inside (black), obtained from the measured dispersion relations. The error bars indicate the standard error of the mean. f, The position xIH of the inner horizon from b. The error bars indicate the standard error of the mean. The linear fit gives vIH = 0.09(1) mm s−1. g, The wavenumber k0 of the short-wavelength superluminal wave between the horizons, found from the location of the peak in the static structure factor computed from the density profiles inside the analogue black hole. The error bars indicate the standard error of the mean. Source data

Source data

Source Data Fig. 3

Plot values including error bars.

Source Data Extended Data Fig. 1

Plot values including error bars.

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Kolobov, V.I., Golubkov, K., Muñoz de Nova, J.R. et al. Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole. Nat. Phys. 17, 362–367 (2021). https://doi.org/10.1038/s41567-020-01076-0

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