Historical research guide · 0465 · 2011
Comment on “Hawking Radiation from Ultrashort Laser Pulse Filaments”
Ralf Schützhold · William G. Unruh
In one minute
In 2010 Daniele Faccio’s group reported photons coming out of fused silica where an intense laser pulse had raised a moving bump in the glass’s refractive index, and read that light as the analogue of Hawking radiation from a horizon. Ralf Schützhold, at Duisburg-Essen, and William Unruh, at British Columbia — the physicist whose 1981 sonic-horizon paper started laboratory analogue gravity — set out four reasons they think the reading is not yet established. In the pulse’s own frame the system is not steady. The photons in question always travel slower than the bump and pass through it, so the setup has a phase horizon but no group-velocity horizon. The phase-horizon condition applies to light moving with the pulse, while the emission was collected at ninety degrees to it. And a Hawking temperature built from the size of the index change predicts photon numbers several orders of magnitude below what was counted. They close by admiring the technique and saying such a set-up may well give the first observation of spontaneous Hawking emission in an analogue system.
Connection
Chapter 5 treats the vacuum as a medium whose excitations can be raised and read in a laboratory, and analogue horizons are the most direct experiment in that programme — so the question of what exactly the Milan and Edinburgh groups detected is a live one, and this is the paper that framed it. It belongs to chapter 1 as well: the exchange is a worked example of how an analogue-gravity claim gets tested, with a named quantity — emission angle, photon number, the presence or absence of a group-velocity horizon — that a next experiment can settle.
From the source
The Hawking effect, as Schützhold and Unruh define it, is thermal radiation at a temperature set by the geometry, emitted by a time-independent system, and caused by the quasi-exponential tearing apart of waves in the vicinity of the horizon; for a white hole it is the time-reversed process, the squeezing of waves. The part of the torn wave packet beyond the horizon can carry negative energy, and the other part then acquires positive energy and constitutes the radiation.Second paragraph, the definition
Of the conditions in that definition, the authors judge that only the last — negative energy beyond the phase horizon, which they relate to the Landau criterion — applies to the filament experiment. On their reading it is an important step towards the observation of Hawking radiation, but not more.Second paragraph, closing sentences
First objection: even in the frame of the pulse the system is not time independent. The pulse lasts a shorter time than the scale set by its own surface gravity, and it carries space-time dependent sub-structure because the phase velocity of the light that makes it differs from the speed of the pulse. In that frame the co-moving photons approach zero frequency, which makes particle creation by the time dependence energetically easy and is closely related to the Landau criterion.Third paragraph, first point
Second objection: there is no exponential tearing by the horizon, because the group velocity of the photons under consideration is always smaller than the speed of the pulse, so they simply pass through it. The authors give the massive-particle dispersion relation as the instructive case — phase velocity above the speed of light, group velocity below it — where a perturbation faster than light has phase horizons but no group horizons, and in a suitable Lorentz frame the same configuration is an instantaneous, time-dependent perturbation with no horizon at all.Fourth paragraph, second point
Third objection: the phase-horizon condition applies only to waves moving in the same direction as the pulse, so Hawking radiation on this account would appear in the forward direction only — whereas the photons were collected at ninety degrees to the pulse. The authors add that the unpolarized character of what was observed seems to rule out scattering of co-moving radiation as the source.Fifth paragraph, third point
Fourth objection, the numbers: taking the Hawking temperature in the pulse frame as Planck’s constant times the gradient of the speed of light in the medium divided by two pi times Boltzmann’s constant, and with a Kerr non-linearity of about one part in a thousand, photons near 800 nanometres would need the index change to vary over a sub-nanometre scale, which the authors find unrealistic when the light making the pulse has a wavelength near 1000 nanometres. The thermal photon number, scaling as the horizon area times the cube of the temperature times the solid angle, with a solid angle of order one hundredth of a radian and a Bessel core a few micrometres across, comes out several orders of magnitude below the counts reported. Schützhold and Unruh nevertheless write that they admire the experimental technique and that such a set-up may well provide the first observation of spontaneous Hawking emission in an analogue system.Sixth and seventh paragraphs, fourth point and closing sentence
The way in
https://doi.org/10.1103/PhysRevLett.107.149401How to cite it
Ralf Schützhold, William G. Unruh (2011) Comment on “Hawking Radiation from Ultrashort Laser Pulse Filaments” doi:10.1103/PhysRevLett.107.149401