# Quantum simulation of black-hole radiation

One of the most striking proposals of Albert Einstein’s general theory of relativity is the prediction of black holes. In 1974, Stephen Hawking suggested that black holes are not completely black, but emit thermal radiation at a temperature that depends on their mass^{1}^{,}^{2}. Astrophysical observations of such Hawking radiation might not be possible, but the physics of the phenomenon should be at play in analogue systems. Writing in *Nature*, de Nova *et al.*^{3} report the detection of Hawking radiation and the measurement of its temperature in an ultracold atomic gas. The results could lead to a better understanding of analogue black holes and Hawking radiation, in general.

Quantum physics tells us that the vacuum of space is not empty, but rather is filled with particles that appear in pairs and then destroy each other immediately. Hawking studied what happens to these particles near a black hole’s event horizon — the boundary beyond which nothing can escape the black hole’s gravitational pull. He found that the particles in a pair could be prevented from destroying each other if they are pulled apart by the tidal forces of gravity. One particle would be absorbed by the black hole and the other would be emitted into space in the form of thermal radiation (Fig. 1a). The absorbed particle, which has negative energy, would reduce the mass of the black hole. Hawking’s finding therefore describes how a black hole can shrink and vanish through a quantum process.

From an astrophysical viewpoint, this process is of great relevance because it decides the fate of black holes in the Universe. However, the temperature that is associated with Hawking radiation, known as the Hawking temperature, is inversely proportional to the mass of the black hole. And for the smallest observed black holes, which have a mass similar to that of the Sun, this temperature^{1} is about 60 nanokelvin. Hawking radiation therefore produces a tiny signal, and it would seem that the phenomenon cannot be verified through observation. However, in 1981, the physicist William Unruh pointed out that Hawking’s discovery can be applied to a wide range of physical systems^{4}, which paved the way for efforts to detect Hawking radiation in the laboratory^{5}.

One way to model the event horizon of a black hole is to use a flowing fluid comprised of ultracold atoms (Fig. 1b). In this approach, part of the fluid travels at a speed that is equal to or greater than the propagation speed of sound waves in the medium. A sound wave that is produced inside this region must follow the fluid flow because it cannot propagate in the opposite direction to the strong current. The outer edge of this area therefore forms an analogue black-hole event horizon. More importantly, the evolution of sound waves in such a fluid can be made to mimic exactly the propagation of classical or quantum fields near a black-hole event horizon^{4}^{–}^{7}. As a result, the fluid can be used as a quantum simulator for black-hole radiation, when it is operated using a high level of control and at sufficiently low temperatures^{8}.

The work of de Nova and colleagues builds on several experimental investigations in which this approach was used to set up analogue black-hole event horizons^{9} to study Hawking radiation^{10}. The authors use a state of matter called a Bose–Einstein condensate that consists of 8,000 rubidium-87 atoms. They use one laser beam to confine the condensate and another to generate a downward potential step — a region in which the potential energy drops sharply. This step moves through the condensate at a constant speed, which is equivalent to the condensate travelling at a constant speed in the reference frame in which the step is stationary. The condensate that flows over the step is accelerated to supersonic speeds, thereby forming an analogue black-hole event horizon.

The authors show that pairs of sound waves are produced at this event horizon. One wave of the pair is emitted away from the supersonic region in the form of Hawking radiation and the other, which has a negative energy, is absorbed into this region (Fig. 1b). Hawking predicted that a black hole will emit radiation that can be described by a single Hawking temperature, dependent only on the mass of the black hole and not on the details of the gravitational field that lies outside the event horizon. The main novelty of de Nova and colleagues’ work is a clever detection scheme that they use to extract the temperature of the emitted radiation. The authors’ findings provide the first evidence of the Hawking temperature from a quantum simulator.

The energy spectra of the emitted radiation lack traces of the microscopic nature of the system^{5}, as well as of macroscopic grey-body corrections. The latter concern the reflection of the emitted radiation back towards the event horizon, owing to an effective potential-energy variation outside the horizon. Such back-reflection is expected to occur for astrophysical black holes. In quantum simulators for black-hole radiation, these microscopic and macroscopic effects can be tuned^{11}, and their absence demonstrates the high level of control that de Nova *et al.* exert over their experimental apparatus. The authors’ set-up is promising, and could be used to investigate many other interesting phenomena — for example, the quantum correlations that are expected to be exhibited by pairs of sound waves produced at the event horizon.

Nature **569**, 634-635 (2019)

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