Quasi-particle creation by analogue black holes

We discuss the issue of quasi-particle production by ``analogue black holes'' with particular attention to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: We show that in order to obtain a stationary and Planckian emission of quasi-particles, it is not necessary to create an ergoregion in the acoustic spacetime (corresponding to a supersonic regime in the flow). It is sufficient to set up a dynamically changing flow either eventually generating an arbitrarily small sonic region v=c, but without any ergoregion, or even just asymptotically, in laboratory time, approaching a sonic regime with sufficient rapidity.Comment: 30 pages, 16 figure

Simulation of Acoustic Black Hole in a Laval Nozzle

A numerical simulation of fluid flows in a Laval nozzle is performed to observe formations of acoustic black holes and the classical counterpart to Hawking radiation under a realistic setting of the laboratory experiment. We determined the Hawking temperature of the acoustic black hole from obtained numerical data. Some noteworthy points in analyzing the experimental data are clarified through our numerical simulation.Comment: 26 pages, published versio

Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates

I study the evolution of mean field and linear quantum fluctuations in a toroidal Bose-Einstein condensate, whose interaction strength is quenched from a finite (repulsive) value to zero. The azimuthal equal-time density-density correlation function is calculated and shows temporal oscillations with twice the (final) excitation frequencies after the transition. These oscillations are a direct consequence of positive and negative frequency mixing during non-adiabatic evolution. I will argue that a time-resolved measurement of the equal-time density correlator might be used to calculate the moduli of the Bogoliubov coefficients and thus the amount of squeezing imposed on a mode, i.e., the number of atoms excited out of the condensate.Comment: 18 pages, IOP styl

Hawking radiation from "phase horizons" in laser filaments?

Belgiorno et al have reported on experiments aiming at the detection of (the analogue of) Hawking radiation using laser filaments [F. Belgiorno et al, Phys. Rev. Lett. 105, 203901 (2010)]. They sent intense focused Bessel pulses into a non-linear dielectric medium in order to change its refractive index via the Kerr effect and saw creation of photons orthogonal to the direction of travel of the pluses. Since the refractive index change in the pulse generated a "phase horizon" (where the phase velocity of these photons equals the pulse speed), they concluded that they observed the analogue of Hawking radiation. We study this scenario in a model with a phase horizon and a phase velocity very similar to that of their experiment and find that the effective metric does not quite correspond to a black hole. The photons created in this model are not due to the analogue of black hole evaporation but have more similarities to cosmological particle creation. Nevertheless, even this effect cannot explain the observations -- unless the pulse has significant small scale structure in both the longitudinal and transverse dimensions.Comment: 13 pages RevTeX, 2 figure

Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole

We provide an experimental demonstration that the circular hydraulic jump represents a hydrodynamic white hole or gravitational fountain (the time-reverse of a black hole) by measuring the angle of the Mach cone created by an object in the "supersonic" inner flow region. We emphasise the general character of this gravitational analogy by showing theoretically that the white hole horizon constitutes a stationary and spatial saddle-node bifurcation within dynamical-systems theory. We also demonstrate that the inner region has a "superluminal" dispersion relation, i.e., that the group velocity of the surface waves increases with frequency, and discuss some possible consequences with respect to the robustness of Hawking radiation. Finally, we point out that our experiment shows a concrete example of a possible "transplanckian distortion" of black/white holes.Comment: 5 pages, 5 figures. New "transplanckian effect" described. Several clarifications, additional figures and references. Published versio

Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio

Emission of correlated photon pairs from superluminal perturbations in dispersive media

We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a process similar to the anomalous Doppler effect: photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in principle possible to engineer the host medium so as to modify the effective group refractive index. In the presence of "fast light" media, e.g. a with group index smaller than unity, a further ~10x enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments would clearly identify the correlated emission of photon pairs.Comment: 9 pages, 7 figure

Causal structure of acoustic spacetimes

The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved spacetime. Specifically, the propagation of acoustic disturbances in moving fluids are described by ``effective metrics'' that carry with them notions of ``causal structure'' as determined by an exchange of sound signals. These acoustic causal structures serve as specific examples of what can be done in the presence of a Lorentzian metric without having recourse to the Einstein equations of general relativity. (After all, the underlying fluid mechanics is governed by the equations of traditional hydrodynamics, not by the Einstein equations.) In this article we take a careful look at what can be said about the causal structure of acoustic spacetimes, focusing on those containing sonic points or horizons, both with a view to seeing what is different from standard general relativity, and to seeing what the similarities might be.Comment: 51 pages, 39 figures (23 colour figures, colour used to convey physics information.) V2: Two references added, some additional discussion of maximal analytic extension, plus minor cosmetic change

Dynamical Aspects of Analogue Gravity: The Backreaction of Quantum Fluctuations in Dilute Bose-Einstein Condensates

We discuss the backreaction force exerted by quantum fluctuations in dilute Bose-Einstein condensates onto the motion of the classical background, derived by an ab initio approach from microscopic physics. It is shown that the effective-action method, widely employed in semiclassical quantum gravity, fails to give the full backreaction force. The failure of the effective-action method is traced back, inter alia, to the problem of the correct choice of the fundamental variables and the related operator ordering issues.Comment: 21+epsilon pages; has appeared in Springer Lecture Notes in Physic

On asymptotically flat solutions of Einstein's equations periodic in time II. Spacetimes with scalar-field sources

We extend the work in our earlier article [4] to show that time-periodic, asymptotically-flat solutions of the Einstein equations analytic at scri, whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptotically-flat solutions analytic at scri, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.Comment: 29 pages, published in Class. Quant. Grav. Replaced. Typos corrected, version which appeared in Class. Quant.Gra