We report numerical evidence of Hawking emission of Bogoliubov phonons from a sonic horizon in a flowing one-dimensional atomic Bose-Einstein condensate. The presence of Hawking radiation is revealed from peculiar long-range patterns in the density-density correlation function of the gas. Quantitative agreement between our fully microscopic calculations and the prediction of analog models is obtained in the hydrodynamic limit. New features are predicted and the robustness of the Hawking signal against a finite temperature discussed.

We have used the analogy between gravitational systems and non-homogeneous fluid flows to calculate the density-density correlation function of an atomic Bose-Einstein condensate in the presence of an acoustic black hole. The emission of correlated pairs of phonons by Hawking-like process results into a peculiar long-range density correlation. Quantitative estimations of the effect are provided for realistic experimental configurations.PACS numbers: 03.75. Gg, 04.62.+v, 04.70.Dy Hawking's prediction of black holes evaporation is generally regarded as a milestone of modern theoretical physics. Combining Einstein's General Relativity and Quantum Mechanics, Hawking was able to show that black holes are not "black", but emit thermal radiation at a temperature inversely proportional to their mass [1]. This quantum mechanical process is triggered by the formation of a horizon and proceeds via the conversion of vacuum fluctuations into on-shell particles. Unfortunately so far there is no experimental support for this amazing theoretical prediction. The emission temperature (Hawking temperature) for a solar mass black hole is expected to be of the order of 10 −8 K, far below the 3 K cosmic microwave background. Nor evidence has been found so far of a X-ray background from a hypothetical primordial population of low mass black holes (∼ 10 10 Kg) in the final stages of their evaporation [2]. Expectations to directly observe Hawking radiation from mini-black holes formed in colliders like LHC or next generation ones, are based on models where the quantum gravity scale (Planck scale: 10 19 GeV) is lowered down to the TeV scale by the presence of extra-dimensions [3]. It is perhaps fair to say that the prospects to have a direct experimental detection of Hawking radiation from black holes in the near future are not very optimistic.In a remarkable work Unruh [4] showed that Hawking radiation is not peculiar to gravity, but is rather a purely kinematic effect of quantum field theory which only depends on field propagation on a black hole-type curved space-time background. This opens the concrete possibility to study the Hawking radiation process in completely different physical systems. As an example, the propagation of sound waves in Eulerian fluids can be described in terms of the same equation describing a massless scalar field on a curved spacetime characterized by an acoustic metric G µν which is function of the background flow: the curvature of the acoustic geometry is induced by the inhomogeneity of the fluid flow, while flat minkowskian spacetime is recovered in the case of a homogeneous system. In particular, an acoustic black hole (or dumb hole) configuration is obtained whenever a subsonic flow turns supersonic: sound waves in the supersonic region are in fact dragged away by the flow and can not propagate back towards the acoustic horizon separating the supersonic and subsonic regions. Upon quantization, Hawking radiation is expected to appear as a flux of thermal phonons emitted from the horizon at a temperature...

In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose-Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their nonrelativistic counterpart. Relativistic condensates exhibit two (rather than one) quasiparticle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show that the metric associated with the massless mode is a generalization of the usual acoustic geometry allowing also for non-conformally flat spatial sections. This is relevant, as it implies that these systems can allow the simulation of a wider variety of geometries. Finally, while in non-RBECs the transition is from Lorentzian to Galilean relativity, these systems represent an emergent gravity toy model where Lorentz symmetry is present (albeit with different limit speeds) at both low and high energies. Hence they could be used as a test field for better understanding the phenomenological implications of such a milder form of Lorentz violation at intermediate energies.

In this Letter we propose to simulate acoustic black holes with ions in rings. If the ions are rotating with a stationary and inhomogeneous velocity profile, regions can appear where the ion velocity exceeds the group velocity of the phonons. In these regions phonons are trapped like light in black holes, even though we have a discrete field theory and a nonlinear dispersion relation. We study the appearance of Hawking radiation in this setup and propose a scheme to detect it.PACS numbers: 04.70. Dy, 04.62.+v, 37.10.Ty In 1974 Hawking showed that the theory of quantum fields in curved spacetime predicts that, surprisingly, black holes emit thermal radiation [1]. Unfortunately, the temperature of this radiation is too small to be detected for typical astrophysical black holes. Furthermore, the original theoretical derivation suffers from the problem that the wave equation is assumed to be valid on all scales, whereas the theory of quantum fields in curved space is assumed to break down at the Planck energy. Unruh showed that the Hawking effect is also manifested in analogous hydrodynamical systems which have a region of supersonic flow and hence a sonic horizon [2]. Such analogous systems offer great advantages, since the effect can potentially be accessible to experiments. Moreover, its robustness can be examined based on the well known microphysics of the hydrodynamical systems. This will contribute to deepen our understanding of the Hawking effect also in gravitational black holes.The hydrodynamic analogy of gravitational spacetimes has inspired many proposals for experimental tests of Hawking radiation in continuous fields in recent years [3], e.g., phonons in Bose-Einstein condensates [4-6], Fermi gases [7], superfluid Helium [8], slow light [9,10], and nonlinear electromagnetic waveguides [11]. So far, no proposal has been physically implemented.In the present work we show how to build an analog model of a black hole in an experimentally realizable system of ions. This is the first experimental proposal in which a discrete system is completely analyzed in the discrete limit (see also [11]). A sublinear dispersion relation at high wave numbers naturally results from the discreteness of the physical system. This affects the trajectories of blue-shifted waves close to the event horizon [12]. The dispersion relation is, additionally, nontrivial at low wave numbers because of the long range Coulomb force. We study how much this affects the appearing Hawking radiation. Explicit numerical calculations show that the Hawking effect is robust against such short scale modifications, e.g., for a continuous field with a sublinear dispersion relation [13] and a discretized field on a falling lattice [14]. Our proposal uses a parameter regime which is accessible in experiments at temperatures currently achieved. Thus, it could lead to the first experimental observation of Hawking radiation.The main idea of our proposal can be summarized as follows. We are constructing a discrete analog of a hydrodynamical system with s...

The backreaction equations for the linearized quantum fluctuations in an acoustic black hole are given. The solution near the horizon, obtained within a dimensional reduction, indicates that acoustic black holes, unlike Schwarzschild ones, get cooler as they radiate phonons. They show remarkable analogies with near-extremal Reissner-Nordström black holes.PACS numbers: 04.62.+v, 04.70.Dy, 47.40.Ki One of the most surprising and far reaching result for its implications in modern theoretical physics is the prediction made by Hawking [1] that black holes emit thermal radiation at a temperature T H proportional to the surface gravity k of the horizon. For a Schwarzschild black hole of mass M , k = (4M ) −1 and T H = (8πM ) −1 (we have set the velocity of light and Boltzman constant equal to one). Hawking obtained this result using quantum field theory in curved space, a scheme for dealing with the matter-gravity system where matter is quantized according to quantum field theory whereas gravity is treated classically according to Einstein General Relativity. The scale at which this framework becomes unreliable is the Planck length where the description of spacetime as a continuous differentiable manifold probably breaks down. Coming back to black holes, because of the quantum emission, they are unstable. Extrapolating Hawking's result (which is strictly valid only for stationary or static black holes) one can conjecture that as the mass decreases, the hole gets hotter and hotter (being the temperature inversely proportional to the mass) and eventually disappears in a time scale of the order of the initial mass to the third power. A more quantitative analysis can be performed by looking at the first order (in ) corrections g (1) αβ to a classical black hole metric g (0) αβ induced by the quantum emission. These can be calculated using the semiclassical Einstein equations [2]Here G µν is the Einstein tensor evaluated for the quan- * Email addresses: balbinot@bo.infn.it, fagnocchi@bo.infn.it † Email address: fabbria@bo.infn.it ‡ Email address: gpp27@cam.ac.uk tum corrected metric g αβ = g (0) αβ + g (1) αβ and linearized in the perturbation g (1) αβ (of order ). The r.h.s. represents the expectation value of the stress tensor for the quantum matter field evaluated in the classical background g (0) αβ . In a very interesting paper, appeared in 1981, Unruh [3] showed that a thermal radiation similar to the one predicted by Hawking for black holes is expected in a completely (at first sight) different physical scenario, namely a fluid undergoing hypersonic motion. This opened the way for the study of condensed matter analogues of Hawking radiation [4], a rather promising field of research where the connections to the experimental side do not seem so remote, compared to gravity.The Eulerian equations of motion for an irrotational and homentropic fluid flow can be derived from the actionwhere ρ is the mass density, ψ the velocity potential, i.e. − → v = − → ∇ψ, u the internal energy density and a dot means time derivative....

We investigate the structure of quantum correlations in an expanding Bose Einstein Condensate (BEC) through the analogue gravity framework. We consider both a 3+1 isotropically expanding BEC as well as the experimentally relevant case of an elongated, effectively 1+1 dimensional, expanding condensate. In this case we include the effects of inhomogeneities in the condensate, a feature rarely included in the analogue gravity literature. In both cases we link the BEC expansion to a simple model for an expanding spacetime and then study the correlation structure numerically and analytically (in suitable approximations). We also discuss the expected strength of such correlation patterns and experimentally feasible BEC systems in which these effects might be detected in the near future.

We investigate the backreaction equations for an acoustic black hole formed in a Laval nozzle under the assumption that the motion of the fluid is one-dimensional. The solution in the near-horizon region shows that as phonons are (thermally) radiated the sonic horizon shrinks and the temperature decreases. This contrasts with the behaviour of Schwarzschild black holes, and is similar to what happens in the evaporation of (near-extremal) Reissner-Nordström black holes (i.e., infinite evaporation time). Finally, by appropriate boundary conditions the solution is extended in both the asymptotic regions of the nozzle.

Using methods developed in Quantum Field Theory in curved space we estimate the effects of the inhomogeneities and of a non vanishing velocity on the depletion of a Bose Einstein condensate within the hydrodynamical approximation.