Nonlocal density correlations as a signature of Hawking radiation from acoustic black holes

Abstract

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...

Quantum correlations across the black hole horizon

“…with u + u ′ = t + t ′ − x * − x ′ * , we see that it has a peak if we regard the the Hawking particle at (x * ) at time t and its in-falling partner is at (x ′ * ) at time t ′ [7]. Due to u ↑ ∞ at the horizon, this correlator vanishes where v = 1.…”

“…For black hole analogues ("dumb holes") in Bose-Einstein condensates, the scalar field φ reflects the phase fluctuations while the momentum density Π corresponds to the density fluctuations δ̺, cf. [7].…”

“…In contrast, the correlations across the horizon, their origin and dependence on the microscopic structure have been studied in far less detail [7].…”

Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: Exact results

“…It involves a model for a Bose-Einstein condensate, BEC, which is arranged to serve as an analog model for a black hole. Similar models have been investigated previously using either analytic approximations or numerical computations [15][16][17][18][19][20][21]. The condensate is approximated as being infinite in length and can be treated as being effectively one-dimensional.…”

Casting New Light on Atomic Interactions

“…Temporal modulation of interactions is theoretically proposed as a route for creating anyonic statistics in optical lattices [1,2] as well as new types of quantum liquids [3,4] and excitations [5][6][7]. Spatial modulation should grant access to unusual soliton behavior [8,9], controlled interfaces between quantum phases [10], stable nonlinear Bloch oscillations [11], and even the dynamics of acoustic black holes [12]. The conventional technique for controlling interactions in cold atoms, magnetic Feshbach resonance [13,14], is typically insufficient for these applications because magnetic coils are generally too large for very fast or local modulation.…”