Abstract
We observe spontaneous Hawking radiation, stimulated by quantum vacuum fluctuations, emanating from an analogue black hole in an atomic Bose–Einstein condensate. Correlations are observed between the Hawking particles outside the black hole and the partner particles inside. These correlations indicate an approximately thermal distribution of Hawking radiation. We find that the high-energy pairs are entangled, while the low-energy pairs are not, within the reasonable assumption that excitations with different frequencies are not correlated. The entanglement verifies the quantum nature of the Hawking radiation. The results are consistent with a driven oscillation experiment and a numerical simulation.
This is a preview of subscription content, access via your institution
Relevant articles
Open Access articles citing this article.
-
Schrödinger–Poisson systems under gradient fields
Scientific Reports Open Access 20 September 2022
-
Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime
Journal of High Energy Physics Open Access 31 January 2022
-
On the assumptions leading to the information loss paradox
Journal of High Energy Physics Open Access 11 October 2021
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Get just this article for as long as you need it
$39.95
Prices may be subject to local taxes which are calculated during checkout






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).
Hawking, S. W. Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460–2473 (1976).
Susskind, L. The paradox of quantum black holes. Nature Phys. 2, 665–677 (2006).
Almheiri, A., Marolf, D., Polchinski, J. & Sully, J. Black holes: complementarity or firewalls? J. High Energy Phys. 2013, 62 (2013).
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).
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).
Barceló, C., Liberati, S. & Visser, M. Analogue gravity from Bose–Einstein condensates. Class. Quantum Gravity 18, 1137–1156 (2001).
Corley, S. & Jacobson, T. Black hole lasers. Phys. Rev. D 59, 124011 (1999).
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).
Giovanazzi, S. Hawking radiation in sonic black holes. Phys. Rev. Lett. 94, 061302 (2005).
Horstmann, B., Reznik, B., Fagnocchi, S. & Cirac, J. I. Hawking radiation from an acoustic black hole on an ion ring. Phys. Rev. Lett. 104, 250403 (2010).
Elazar, M., Fleurov, V. & Bar-Ad, S. All-optical event horizon in an optical analog of a Laval nozzle. Phys. Rev. A 86, 063821 (2012).
Solnyshkov, D. D., Flayac, H. & Malpuech, G. Black holes and wormholes in spinor polariton condensates. Phys. Rev. B 84, 233405 (2011).
Busch, X. & Parentani, R. Quantum entanglement in analogue Hawking radiation: When is the final state nonseparable? Phys. Rev. D 89, 105024 (2014).
Finazzi, S. & Carusotto, I. Entangled phonons in atomic Bose–Einstein condensates. Phys. Rev. A 90, 033607 (2014).
Steinhauer, J. Measuring the entanglement of analogue Hawking radiation by the density–density correlation function. Phys. Rev. D 92, 024043 (2015).
de Nova, J. R. M., Sols, F. & Zapata, I. Violation of Cauchy–Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures. Phys. Rev. A 89, 043808 (2014).
Doukas, J., Adesso, G. & Fuentes, I. Ruling out stray thermal radiation in analogue black holes. Preprint at http://arXiv.org/abs/1404.4324 (2014).
Boiron, D. et al. Quantum signature of analog Hawking radiation in momentum space. Phys. Rev. Lett. 115, 025301 (2015).
de Nova, J. R. M., Sols, F. & Zapata, I. Entanglement and violation of classical inequalities in the Hawking radiation of flowing atom condensates. New J. Phys. 17, 105003 (2015).
Lahav, O. et al. Realization of a sonic black hole analog in a Bose–Einstein condensate. Phys. Rev. Lett. 105, 240401 (2010).
Shammass, I., Rinott, S., Berkovitz, A., Schley, R. & Steinhauer, J. Phonon dispersion relation of an atomic Bose–Einstein condensate. Phys. Rev. Lett. 109, 195301 (2012).
Schley, R. et al. Planck Distribution of Phonons in a Bose–Einstein Condensate. Phys. Rev. Lett. 111, 055301 (2013).
Steinhauer, J. Observation of self-amplifying Hawking radiation in an analogue black-hole laser. Nature Phys. 10, 864–869 (2014).
Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).
Belgiorno, F. et al. Hawking radiation from ultrashort laser pulse filaments. Phys. Rev. Lett. 105, 203901 (2010).
Unruh, W. & Schützhold, R. Hawking radiation from ‘phase horizons’ in laser filaments? Phys. Rev. D 86, 064006 (2012).
Liberati, S., Prain, A. & Visser, M. Quantum vacuum radiation in optical glass. Phys. Rev. D 85, 084014 (2012).
Nguyen, H. S. et al. Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons. Phys. Rev. Lett. 114, 036402 (2015).
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).
Parentani, R. From vacuum fluctuations across an event horizon to long distance correlations. Phys. Rev. D 82, 025008 (2010).
Pines, D. & Nozières, Ph. The Theory of Quantum Liquids Vol. I, Section 2.1 (Addison-Wesley, 1988).
Nozières, Ph. & Pines, D. The Theory of Quantum Liquids Vol. II, Section 3.1 (Addison-Wesley, 1990).
Pitaevskii, L. & Stringari, S. Bose–Einstein Condensation Section 12.9 (Oxford Univ. Press, 2003).
Acknowledgements
I thank R. Parentani, W. Unruh, F. Michel, N. Pavloff and A. Fabbri for helpful comments. This work was supported by the Israel Science Foundation.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The author declares no competing financial interests.
Rights and permissions
About this article
Cite this article
Steinhauer, J. Observation of quantum Hawking radiation and its entanglement in an analogue black hole. Nature Phys 12, 959–965 (2016). https://doi.org/10.1038/nphys3863
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys3863
This article is cited by
-
Schrödinger–Poisson systems under gradient fields
Scientific Reports (2022)
-
Horizons and correlation functions in 2D Schwarzschild-de Sitter spacetime
Journal of High Energy Physics (2022)
-
Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole
Nature Physics (2021)
-
What we cannot learn from analogue experiments
Synthese (2021)
-
Quantum unitary dynamics of a charged fermionic field and Schwinger effect
Journal of High Energy Physics (2021)