Historical research guide · 0791 · 2014

Observation of self-amplifying Hawking radiation in an analogue black-hole laser

Jeff Steinhauer

In one minute

Jeff Steinhauer swept a laser-made potential step through an elongated rubidium Bose–Einstein condensate. In the step’s frame, the atoms flow across it and pass the speed of sound, forming an outer sonic horizon; farther along they slow, forming an inner horizon. Sound-wave partners trapped between the two horizons can return to the outer one and stimulate further emission. Steinhauer imaged density patterns as the system evolved. Correlations revealed an outgoing band beyond the outer horizon and a standing wave between the horizons. The standing wave grew exponentially, the behavior predicted for a black-hole laser. Using its growth time and the waves’ round-trip time, the paper inferred roughly three emitted Hawking phonons per returning negative-energy mode. These are excitations of a laboratory fluid, not radiation from an astrophysical black hole.

Connection

Steinhauer built two sonic horizons in one flowing condensate. The outgoing correlation band and exponentially growing standing wave test the predicted feedback between them. The experiment shows how an inner horizon can amplify analogue Hawking emission in a laboratory fluid.

From the source

A step-like ‘waterfall’ potential made by a knife-edged laser beam accelerates the condensate past its own speed of sound, creating an outer horizon; further downstream the flow climbs the trap and drops back below the speed of sound, creating an inner horizon. That two-horizon arrangement is the analogue of a charged black hole, and it is what makes lasing possible.Fig. 1c and the experimental description following it
The escaping Hawking radiation is seen directly in the density–density correlation function as bands extending beyond the outer horizon into the subsonic region — the output of the black-hole laser — while the region between the horizons shows the checkerboard pattern predicted for a standing negative-energy mode.Fig. 4, panels a to g; the paragraph naming the escaping flux
The amplitude of that mode grows exponentially in time, which is what separates a black-hole laser from the alternatives: a single horizon gives no growth, white-hole radiation gives linear or logarithmic growth, and white-hole undulations give no growth.Fig. 5; the paragraph beginning ‘The scale of Fig. 5 is logarithmic’
From the ratio of the lasing growth time to the round-trip time between horizons, the paper infers roughly three Hawking phonons produced for each negative-energy mode returning to the outer horizon. The inferred dimensionless ratio ℏω/(k_B T_H) is about 0.3, comparing the lasing-mode energy with the energy scale set by the Hawking temperature.Eqs. (1) and (3); Fig. 6b and 6c; Conclusion
The starting state is quantum rather than thermal. The measured static structure factor falls as the wavenumber falls, the opposite of a thermally dominated gas, putting the initial temperature between zero and about a tenth of the chemical potential — a thermal fraction of about two parts in a hundred thousand.Fig. 3b and the paragraph on the static structure factor
Steinhauer turns the result outward: strong laser-like Hawking radiation seen coming from a real astrophysical black hole would imply both an inner horizon and a dispersion relation that curves upward at short wavelength, and the same apparatus is proposed as a platform for simulating the expansion of the early universe.Conclusion, final paragraph

The way in

https://doi.org/10.1038/nphys3104

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Licence checked directly. Published as Nature Physics 10, 864–869 (2014); the Crossref record for the DOI carries only Springer Nature’s text-and-data-mining terms. The author version is on arXiv as 1409.6550, submitted 23 September 2014 with a second version on 9 November 2014 correcting one equation, and the arXiv record states the arXiv.org perpetual non-exclusive distribution licence — not a Creative Commons licence, checked on the arXiv abstract page on 2026-09-08. So this sheet carries the summary, the claims and Steinhauer’s own abstract and sends the reader to the source. The claims below were written from the arXiv text, whose figure numbering the locators use; that version is titled ‘Observation of self-amplifying Hawking radiation in an analog black hole laser’. Steinhauer works in the Department of Physics at the Technion, Israel Institute of Technology, Haifa; the work was supported by the Russell Berrie Nanotechnology Institute and the Israel Science Foundation. Three companion sheets in this library carry the rest of this line of work: Finazzi and Parentani’s theory paper ‘Black hole lasers in Bose–Einstein condensates’, New Journal of Physics 12, 095015 (2010), at /library/stm-b057755b99; Steinhauer’s ‘Observation of quantum Hawking radiation and its entanglement in an analogue black hole’, Nature Physics 12, 959 (2016), at /library/stm-a3449e5f7e; and Muñoz de Nova, Golubkov, Kolobov and Steinhauer’s ‘Observation of thermal Hawking radiation and its temperature in an analogue black hole’, Nature 569, 688 (2019), at /library/stm-95010a1182.

How to cite it

Jeff Steinhauer (2014) Observation of self-amplifying Hawking radiation in an analogue black-hole laser doi:10.1038/nphys3104

Where it sits in the curriculum

The vacuum as a quantum fluid