Experimental black hole evaporation

In 1974 Stephen Hawking argued that black holes are not black. Due to a still poorly understood quantum instability near the horizon, he calculated that a black hole will continuously emit radiation with a thermal spectrum. The temperature is inversely proportional to the mass of the black hole (about 10^-7 K for a solar-mass black hole).

Hawking’s idea will not soon be testable on astrophysical black holes. But in a 1981 paper , I suggested that analogs to the horizon and to the Hawking process could exist for other waves. Irrotational flow of a fluid, such that a surface exists where the velocity of the fluid equals that of sound, would act as a (sonic) horizon analog. Hawking’s argument would predict that an analog black hole would also emit quantum thermal radiation at the horizon. Such “dumb” (not able to speak) holes could thus be a test of the assumptions that went into Hawking’s black hole calculations.

Since then, many other systems with horizons have been shown, theoretically, to display thermal emission. But over the past several years, scientists have also carried out horizon-temperature experiments. In 2011 Silke Weinfurtner and colleagues at the University of British Columbia (including myself) measured the surface waves in flowing water near a horizon. Using stimulated emission experiments, we showed , via Einstein’s relation between stimulated and spontaneous emission, that the spontaneous quantum emission from that horizon would be thermal. The latest and most impressive work comes from Jeff Steinhauer at the Technion–Israel Institute of Technology, whose 15 August paper reports detecting the spontaneous emission of the sonic analog of quantum-entangled Hawking radiation in a Bose–Einstein condensate (BEC). Although Steinhauer’s claim needs to be verified, his dumb-hole horizon could be the first direct experimental evidence that horizons have a quantum-induced temperature.

Luis Garay and collaborators demonstrated that a BEC has many advantages for creating dumb holes. Not only can it be cooled to about 10^–12 K, but the equation of motion of the BEC, the time-dependent Gross–Pitaevskii equation, can be written as a pair of fluid equations that are almost identical to those in my 1981 paper. The only difference is that the BEC’s equation contains an additional “quantum pressure” term, which changes the velocity of sound at wavelengths shorter than a certain scale called the healing length. Thus, although at long wavelengths sound in a BEC is a good analog to light (whose velocity is wavelength independent), it deviates at shorter wavelengths.

Steinhauer’s BEC setup (less than 100 μm long) is converted into one with a sonic horizon by shining a laser beam with a sharp edge onto the BEC. The laser frequency is such that the atoms are accelerated into the region with the strong laser field. The sharp leading edge of the laser field is arranged to travel along the BEC with a velocity slightly less than the velocity of sound in the stationary BEC, but greater than that of sound in the BEC in the laser field, forming a sonic horizon. In the frame of the advancing edge, upstream sound in both the dark region and in the laser-illuminated region travels away from the horizon. Thus no sound can escape from behind the horizon, just as outgoing light cannot exit a black hole.

Roberto Balbinot at the University of Bologna in Italy and colleagues had suggested that one way to detect quantum emission in a BEC is to look at the density–density correlation function near the horizon. For any field obeying a linear equation (such as for the sound waves in a BEC and the fields around astrophysical black holes), particles are created in entangled pairs, with one escaping away from the horizon and the other trapped inside. By measuring the correlation of fluctuations in the densities on both sides of the horizon, Steinhauer could look for evidence of the entangled sound-wave phonon pairs escaping from his tabletop horizon.

Running the experiment thousands of times, Steinhauer determined the correlation function and used it to obtain an entanglement measure. A positive value for this measure denotes entanglement, a purely quantum property. Assuming that the downstream sound is in its vacuum state, he found that, for short wavelengths (but still long enough that the analogy to light is good), the measure is positive. That would imply that the fluctuations are of quantum origin and are caused by particles emanating from the horizon. The structure of the correlation function is also consistent (albeit with large uncertainty) with thermal emission.

Steinhauer’s experiment clearly needs to be confirmed by others, with assurance that there is no other explanation for the structure of the density–density correlation function. I think there is a reasonable probability that Steinhauer is right. Since the theoretical horizon-temperature in the BEC is derived in the same way that Hawking derived the black hole temperature, this experiment would then support the results of Hawking’s calculation for black hole temperature.

How much further could the analogy be pushed? Planck-scale physics (quantum gravity) is unknown. The physics of fluids on scales much shorter than the mean distance between atoms (such as in liquid helium) is also poorly understood. In Hawking’s derivation, the initial vacuum fluctuations that produce the thermal radiation for black holes are at scales far shorter than the Planck length, where we do not trust theory. In fact, we believe that black hole thermal radiation is independent of Planck-scale physics. That belief would be strengthened if an experiment showed that the thermal radiation emitted by the BEC horizon originated from vacuum fluctuations at scales shorter than the interatomic separation.

Steinhauer’s experiment, if correct, already indicates that the temperature and the entanglement are independent of the changes in sound velocity that occur at wavelengths shorter than the healing length. The result suggests that black hole radiation is independent of the behavior of the theory on short scales (sub-Planck-scale), contrary to Hawking’s derivation. It is thus a theoretical challenge to produce a derivation that makes clear what is really needed to produce such thermal radiation at the horizon. Experiments certainly could show us how to do this.

The next experimental challenge is to redo the BEC experiments to confirm and improve these results. Is the spectrum truly thermal? Is the lack of long-wavelength entanglement due to the excitation of other modes, and can it be measured? Which other physical systems show the effect? The next demonstration is likely to be in an optical system, such as the experiments with diamond being conducted by Daniele Faccio’s group at Heriot-Watt University in Edinburgh, Scotland. Finally, under what conditions do the analogies break down?

My original 1981 paper was titled “Experimental black-hole evaporation?” I fought hard with the editors of Physical Review Letters to keep the question mark, since the possibility of such experiments seemed so remote. To my surprise and gratification, black hole evaporation has become experimental. No question mark needed.

William Unruh is a theoretical physicist at the University of British Columbia in Vancouver, Canada. His contributions to the understanding of gravity, black holes, cosmology, quantum fields in curved spaces, and the foundations of quantum mechanics include the discovery of the Unruh effect .