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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
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.
References
Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973).
Hawking, S. W. Black hole explosions? Nature 248, 30–31 (1974).
Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975).
Dimopoulos, S. & Landsberg, G. Black holes at the Large Hadron Collider. Phys. Rev. Lett. 87, 161602 (2001).
Giddings, S. B. & Thomas, S. High energy colliders as black hole factories: the end of short distance physics. Phys. Rev. D 65, 056010 (2002).
Page, D. N. Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole. Phys. Rev. D 13, 198–206 (1976).
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).
Rousseaux, G., Mathis, C., Maïssa, P., Philbin, T. G. & Leonhardt, U. Observation of negative-frequency waves in a water tank: a classical analogue to the Hawking effect? New J. Phys. 10, 053015 (2008).
Euvé, L. -P., Michel, F., Parentani, R., Philbin, T. G. & Rousseaux, G. Observation of noise correlated by the Hawking effect in a water tank. Phys. Rev. Lett. 117, 121301 (2016).
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).
Unruh, W. G. Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351–1353 (1981).
Garay, L. J., Anglin, J. R., Cirac, J. I. & Zoller, P. Sonic analog of gravitational black holes in Bose–Einstein condensates. Phys. Rev. Lett. 85, 4643–4647 (2000).
Visser, M. Acoustic black holes: horizons, ergospheres and Hawking radiation. Class. Quantum Gravity 15, 1767–1791 (1998).
Balbinot, R., Fabbri, A., Fagnocchi, S., Recati, A. & Carusotto, I. Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes. Phys. Rev. A 78, 021603(R) (2008).
Carusotto, I., Fagnocchi, S., Recati, A., Balbinot, R. & Fabbri, A. Numerical observation of Hawking radiation from acoustic black holes in atomic Bose–Einstein condensates. New J. Phys. 10, 103001 (2008).
Macher, J. & Parentani, R. Black-hole radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043601 (2009).
Larré, P. -É., Recati, A., Carusotto, I. & Pavloff, N. Quantum fluctuations around black hole horizons in Bose–Einstein condensates. Phys. Rev. A 85, 013621 (2012).
Recati, A., Pavloff, N. & Carusotto, I. Bogoliubov theory of acoustic Hawking radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043603 (2009).
Steinhauer, J. Measuring the entanglement of analogue Hawking radiation by the density–density correlation function. Phys. Rev. D 92, 024043 (2015).
Jacobson, T. A. & Volovik, G. E. Event horizons and ergoregions in 3He. Phys. Rev. D 58, 064021 (1998).
Schützhold, R. & Unruh, W. G. Hawking radiation in an electromagnetic waveguide? Phys. Rev. Lett. 95, 031301 (2005).
de Nova, J. R. M., Guéry-Odelin, D., Sols, F. & Zapata, I. Birth of a quasi-stationary black hole in an outcoupled Bose–Einstein condensate. New J. Phys. 16, 123033 (2014).
Balbinot, R., Fagnocchi, S., Fabbri, A. & Procopio, G. P. Backreaction in acoustic black holes. Phys. Rev. Lett. 94, 161302 (2005).
Steinhauer, J. Observation of quantum Hawking radiation and its entanglement in an analogue black hole. Nat. Phys. 12, 959–965 (2016).
de Nova, J. R. M., 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).
Giovanazzi, S. Entanglement entropy and mutual information production rates in acoustic black holes. Phys. Rev. Lett. 106, 011302 (2011).
Brout, R., Massar, S., Parentani, R. & Spindel, P. A primer for black hole quantum physics. Phys. Rep. 260, 329–446 (1995).
Isoard, M. & Pavloff, N. Departing from thermality of analogue Hawking radiation in a Bose–Einstein condensate. Phys. Rev. Lett. 124, 060401 (2020).
Wang, Y. -H., Jacobson, T., Edwards, M. & Clark, C. W. Mechanism of stimulated Hawking radiation in a laboratory Bose–Einstein condensate. Phys. Rev. A 96, 023616 (2017).
Tettamanti, M., Cacciatori, S. L., Parola, A. & Carusotto, I. Numerical study of a recent black-hole lasing experiment. EPL 114, 60011 (2016).
Nozières, P. & Pines, D. The Theory of Quantum Liquids Vol. II, Ch. 5 (Addison-Wesley, 1990).
Wang, Y. -H., Jacobson, T., Edwards, M. & Clark, C. W. Induced density correlations in a sonic black hole condensate. SciPost Phys. 3, 022 (2017).
Corley, S. & Jacobson, T. Black hole lasers. Phys. Rev. D 59, 124011 (1999).
Volovik, G. E. Black hole and Hawking radiation by type-II Weyl fermions. JETP Lett. 104, 645–648 (2016).
Lahav, O. et al. Realization of a sonic black hole analog in a Bose–Einstein condensate. Phys. Rev. Lett. 105, 240401 (2010).
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
Authors and Affiliations
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
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
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 Fig. 3
Plot values including error bars.
Source Data Extended Data Fig. 1
Plot values including error bars.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-020-01076-0
