Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of quantum Hawking radiation and its entanglement in an analogue black hole


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Hawking radiation and entanglement in the gravitational analogy.
Figure 2: The analogue black hole.
Figure 3: Oscillating horizon experiment.
Figure 4: Observation of Hawking/partner pairs.
Figure 5: The measured population of the Hawking radiation.
Figure 6: Observation of entanglement between the Hawking pairs.


  1. 1

    Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973).

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    Hawking, S. W. Black hole explosions? Nature 248, 30–31 (1974).

    ADS  Article  Google Scholar 

  3. 3

    Hawking, S. W. Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Hawking, S. W. Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460–2473 (1976).

    ADS  MathSciNet  Google Scholar 

  5. 5

    Susskind, L. The paradox of quantum black holes. Nature Phys. 2, 665–677 (2006).

    ADS  Article  Google Scholar 

  6. 6

    Almheiri, A., Marolf, D., Polchinski, J. & Sully, J. Black holes: complementarity or firewalls? J. High Energy Phys. 2013, 62 (2013).

    MathSciNet  Article  Google Scholar 

  7. 7

    Unruh, W. G. Experimental black-hole evaporation? Phys. Rev. Lett. 46, 1351–1353 (1981).

    ADS  Article  Google Scholar 

  8. 8

    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).

    ADS  Article  Google Scholar 

  9. 9

    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).

    ADS  Article  Google Scholar 

  10. 10

    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).

    ADS  Article  Google Scholar 

  11. 11

    Macher, J. & Parentani, R. Black-hole radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043601 (2009).

    ADS  Article  Google Scholar 

  12. 12

    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).

    ADS  Article  Google Scholar 

  13. 13

    Recati, A., Pavloff, N. & Carusotto, I. Bogoliubov theory of acoustic Hawking radiation in Bose–Einstein condensates. Phys. Rev. A 80, 043603 (2009).

    ADS  Article  Google Scholar 

  14. 14

    Barceló, C., Liberati, S. & Visser, M. Analogue gravity from Bose–Einstein condensates. Class. Quantum Gravity 18, 1137–1156 (2001).

    ADS  MathSciNet  Article  Google Scholar 

  15. 15

    Corley, S. & Jacobson, T. Black hole lasers. Phys. Rev. D 59, 124011 (1999).

    ADS  MathSciNet  Article  Google Scholar 

  16. 16

    Jacobson, T. A. & Volovik, G. E. Event horizons and ergoregions in 3He. Phys. Rev. D 58, 064021 (1998).

    ADS  Article  Google Scholar 

  17. 17

    Schützhold, R. & Unruh, W. G. Hawking radiation in an electromagnetic waveguide? Phys. Rev. Lett. 95, 031301 (2005).

    ADS  Article  Google Scholar 

  18. 18

    Giovanazzi, S. Hawking radiation in sonic black holes. Phys. Rev. Lett. 94, 061302 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  19. 19

    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).

    ADS  Article  Google Scholar 

  20. 20

    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).

    ADS  Article  Google Scholar 

  21. 21

    Solnyshkov, D. D., Flayac, H. & Malpuech, G. Black holes and wormholes in spinor polariton condensates. Phys. Rev. B 84, 233405 (2011).

    ADS  Article  Google Scholar 

  22. 22

    Busch, X. & Parentani, R. Quantum entanglement in analogue Hawking radiation: When is the final state nonseparable? Phys. Rev. D 89, 105024 (2014).

    ADS  Article  Google Scholar 

  23. 23

    Finazzi, S. & Carusotto, I. Entangled phonons in atomic Bose–Einstein condensates. Phys. Rev. A 90, 033607 (2014).

    ADS  Article  Google Scholar 

  24. 24

    Steinhauer, J. Measuring the entanglement of analogue Hawking radiation by the density–density correlation function. Phys. Rev. D 92, 024043 (2015).

    ADS  Article  Google Scholar 

  25. 25

    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).

    ADS  Article  Google Scholar 

  26. 26

    Doukas, J., Adesso, G. & Fuentes, I. Ruling out stray thermal radiation in analogue black holes. Preprint at (2014).

  27. 27

    Boiron, D. et al. Quantum signature of analog Hawking radiation in momentum space. Phys. Rev. Lett. 115, 025301 (2015).

    ADS  Article  Google Scholar 

  28. 28

    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).

    ADS  Article  Google Scholar 

  29. 29

    Lahav, O. et al. Realization of a sonic black hole analog in a Bose–Einstein condensate. Phys. Rev. Lett. 105, 240401 (2010).

    ADS  Article  Google Scholar 

  30. 30

    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).

    ADS  Article  Google Scholar 

  31. 31

    Schley, R. et al. Planck Distribution of Phonons in a Bose–Einstein Condensate. Phys. Rev. Lett. 111, 055301 (2013).

    ADS  Article  Google Scholar 

  32. 32

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

    ADS  Article  Google Scholar 

  33. 33

    Philbin, T. G. et al. Fiber-optical analog of the event horizon. Science 319, 1367–1370 (2008).

    ADS  Article  Google Scholar 

  34. 34

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

    ADS  Article  Google Scholar 

  35. 35

    Unruh, W. & Schützhold, R. Hawking radiation from ‘phase horizons’ in laser filaments? Phys. Rev. D 86, 064006 (2012).

    ADS  Article  Google Scholar 

  36. 36

    Liberati, S., Prain, A. & Visser, M. Quantum vacuum radiation in optical glass. Phys. Rev. D 85, 084014 (2012).

    ADS  Article  Google Scholar 

  37. 37

    Nguyen, H. S. et al. Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons. Phys. Rev. Lett. 114, 036402 (2015).

    ADS  Article  Google Scholar 

  38. 38

    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).

    ADS  Article  Google Scholar 

  39. 39

    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).

    ADS  Article  Google Scholar 

  40. 40

    Parentani, R. From vacuum fluctuations across an event horizon to long distance correlations. Phys. Rev. D 82, 025008 (2010).

    ADS  Article  Google Scholar 

  41. 41

    Pines, D. & Nozières, Ph. The Theory of Quantum Liquids Vol. I, Section 2.1 (Addison-Wesley, 1988).

    MATH  Google Scholar 

  42. 42

    Nozières, Ph. & Pines, D. The Theory of Quantum Liquids Vol. II, Section 3.1 (Addison-Wesley, 1990).

    MATH  Google Scholar 

  43. 43

    Pitaevskii, L. & Stringari, S. Bose–Einstein Condensation Section 12.9 (Oxford Univ. Press, 2003).

    MATH  Google Scholar 

Download references


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



Corresponding author

Correspondence to Jeff Steinhauer.

Ethics declarations

Competing interests

The author declares no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Further reading


Quick links