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Physicists stimulate Hawking radiation from optical analogue of a black hole

19 Jan 2019
Artistic impression of a black hole at the centre of a swirling cloud of stars and galaxies
(CC BY-SA Alain r)

Stephen Hawking liked to claim that, if his most famous prediction had been verified experimentally, he would have won a Nobel prize. The prediction was that, as he once put it, “black holes ain’t so black”. These stars, which collapse to an infinitely dense singularity, can emit intense radiation from just outside their event horizon – the point of no return beyond which even light can’t escape from the intense gravity.

Few doubt that this Hawking radiation, predicted in 1974, is a real phenomenon – but no-one has ever seen it. Direct astronomical observations are very challenging because the radiation is too feeble; the X-rays streaming from suspected black holes are instead emitted by incredibly hot gas as it spirals inwards. But researchers believe that the equivalent of Hawking radiation might be seen emerging from laboratory experiments that mimic black holes in other media, such as light, acoustic or water waves. Now, a team at the Weizmann Institute of Science in Rehovot, Israel, has reported experiments that they say come one step closer to producing Hawking radiation in an “optical black hole”.

Virtual particles drive Hawking radiation

Hawking radiation is caused by quantum events near the event horizon. According to quantum theory, the vacuum of empty space is alive with “virtual particles”: pairs comprised of a subatomic particle and its antiparticle (such as an electron and positron), which may pop briefly into existence in a random quantum fluctuation before annihilating one another. But at the event horizon, one of the pair might fall into the back hole while the other escapes and becomes a real particle. This process draws gravitational energy from the black hole, in effect lowering its mass. In this way the black hole slowly evaporates as Hawking radiation streams from its surface.

In laboratory analogues of black holes, researchers create a kind of event horizon in a wave medium such as light or sound, within which region waves cannot escape. These systems are not gravitational at all, but the mathematics describing them is formally equivalent to the equations of general relativity that apply to black holes. Such analogues were first proposed in 1981 by William Unruh of the University of British Columbia in Vancouver, Canada, who explained how they might be mimicked by sound waves in a flowing liquid.

The fact that both the mathematics is so similar and that observations in the analogues are what is predicted gives, to me at least, additional weight to Hawking’s predictions.

William Unruh, University of British Columbia

These systems, Unruh showed, can have an equivalent of Hawking radiation, in this case corresponding to a particular spectrum of sound waves emitted from a “sonic horizon”. Optical physicist Ulf Leonhardt, who led the new study, comments: “Hawking radiation is a much more general phenomenon than originally thought. It can happen whenever event horizons are made, be it in astrophysics or for light in optical materials, water waves or ultracold atoms.”

Possible analogues stimulate debate

Several different systems have been explored as black-hole analogues, but observing Hawking radiation from them has proved difficult and contentious. “Observations of analogues of Hawking radiation in the laboratory seem to have been vexed with problems,” says Leonhardt.

The first claims, reported in a fibre-optic system, turned out to come from a different optical effect similar to Cherenkov radiation. Soon after, Unruh and coworkers used water waves, but there were ambiguities in the interpretation of the results. Researchers in France who replicated the experiment concluded that the observed effect was not simply Hawking radiation. That group, however, claimed to see the fluid-dynamical equivalent of Hawking radiation in experiments in a water tank in 2016.

Meanwhile, Jeff Steinhauer of the Technion-Israel Institute of Technology in Haifa reported an experiment on a cloud of ultracold atoms held in a collective quantum state called a Bose-Einstein condensate (BEC), in which he claimed that a black-hole analogue showed self-amplifying Hawking radiation: a kind of lasing. But this experiment too has drawn criticism, although Steinhauer stands by his claim.

Meanwhile in 2016 Steinhauer claimed to have observed Hawking radiation and the entanglement between the Hawking partners (one outside and other one inside the horizon) in the same BEC system. “This paper was widely reported in the press as the final proof of Hawking’s prediction, but it is questionable,” says Leonhardt. He says that a new preprint by Steinhauer and his co-authors “looks much better – this is the first one I would begin to believe”.

Unruh comments: “There is now a competition between BECs and optical systems for the first unarguable sighting of spontaneous emission of Hawking radiation by an event horizon.”

“I greatly admire the heroism and skill of the people doing this work, but it’s a difficult subject,” says Leonhardt.

Towards an optical event horizon

Leonhardt’s team has now claimed not quite the ultimate goal of seeing spontaneous Hawking radiation from an optical black hole, but a “milestone” towards it: the stimulation of such radiation by an external probe beam. Such stimulated emission was in fact what Unruh and colleagues claimed in their experiments on water waves in 2011. “Einstein noted in 1919 that there is a very close link between spontaneous emission and stimulated emission, in that the latter implies the former,” says Unruh.

In the optical analogue experiment, a short and intense pulse of light travelling in an optical medium like a fibre produces a change in refractive index of the medium because of nonlinear effects. This can appear to bring light in the fibre to a standstill at the leading edge of the pump pulse: an optical event horizon. The analogue of Hawking radiation shows up as light emitted from the horizon that contains “negative frequencies”, which means that the photons – like virtual particles falling into a black hole horizon – have negative energies. This shows up as a signature in the output light from the fibre: in effect it means energy is drawn from the pump pulse.

In the Weizmann team’s experiment, a second “probe” pulse stimulates this emission. In other words, the probe injects fluctuations – they don’t arise spontaneously. “The probe plays the role of vacuum fluctuations, but has an amplitude we can make reasonably large without destroying the effect,” Leonhardt explains.

But he admits that there is still a problem his team doesn’t fully understand. “Our numerical calculations predict a much stronger Hawking light than we have seen,” he says. He thinks this might arise from the way the fibre can support other, unwanted modes at ultraviolet frequencies. “We plan to investigate this next,” he says. “But we are open to surprises and will remain our own worst critics.”

No easy answers

Sergio Cacciatori of the University of Insubria in Italy, who has participated in some of the earlier studies of analogues of Hawking radiation, says that the results are hard to assess because the optical model of a black hole is rather complicated. In particular, different frequencies each see a different effective “speed of light” and therefore a different event horizon. “The community needs to agree on what exactly the definition of Hawking radiation should be [in such an experiment],” he says.

“The advantage of working with an optical system is that, among all the possible analogue setups, these are the only ones allowing the possibility to detect Hawking photons directly,” he adds. “But it is more difficult to identify what exactly Hawking photons are in this case.”

What’s more, he says, the stimulated emission seen here is a classical effect that does not derive for certain from amplification of the analogue of spontaneous Hawking radiation – it could just be amplifying other classical sources of emission. Leonhardt, however, says that his team has checked carefully for other potential sources of the radiation. “We are confident that we are seeing the real thing, and are not falling for a red herring,” he says.

Would the unambiguous sighting of spontaneous Hawking radiation from one of these laboratory analogues validate Hawking’s prediction anyway? That is maybe a matter of taste. “While it is obvious that the behaviour in fluids [and optics] is not the same as the behaviour in spacetime,” says Unruh, “the fact that both the mathematics is so similar and that observations in the analogues are what is predicted gives, to me at least, additional weight to Hawking’s predictions.”

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