Arising out of a Non-local non-relativistic BEC, we present an Analogue gravity model upto $\mathcal{O}(ξ^{2})$ accuracy in the presence of the quantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime where the series solution of the free minimally coupled KG equation for the large length scale massive scalar modes is derived. We systematically address the issues of the presence of the quantum potential term being the root cause of a UV-IR coupling between short wavelength `primary' modes which are supposedly Hawking radiated through the sonic horizon and the large wavelength `secondary' modes. In the quantum gravity experiments of analogue Hawking radiation in the laboratory, this UV-IR coupling is inevitable and one can not get rid of these large wavelength excitations which would grow over space by gaining energy from the short wavelength Hawking radiated modes. We identify the characteristic feature in the growth rate(s) that would distinguish these primary and secondary modes.
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 determine the feasibility of detecting analogue Hawking radiation in a Bose-Einstein condensate in the presence of atom loss induced heating. We find that phonons created by three-body losses overshadow those due to analogue Hawking radiation. To overcome this problem, three-body losses may have to be suppressed, for example as proposed by Search et al. [Phys. Rev. Lett. 92 140401 (2004)]. The reduction of losses to a few percent of their normal rate is typically sufficient to suppress the creation of loss phonons on the time scale of a fast analogue Hawking phonon detection.
Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon…
We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a 1+1-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.
In this paper we extend the hydrodynamic results of [1] and study, analytically, the propagation of Bogoliubov phonons on top of Bose-Einstein condensates with step-like discontinuities by taking into account dispersion effects. We focus on the Hawking signal in the density-density correlations in the formation of acoustic black hole-like configurations.
In this paper we consider possible analogue Hawking radiation from a normal dielectric and metamaterial composite, having an analogue horizon where the dielectric parameters vanish and change sign upon crossing this transition zone. We follow a complex path analysis to show the presence of an analogue Hawking temperature at the horizon and subsequent photon production from the ambient electromagnetic field. Possibility of experimental observation is also commented upon.
We present a detailed analytical analysis of the propagation of Bogoliubov phonons on top of Bose-Einstein condensates with spatial and temporal step-like discontinuities in the hydrodynamic limit and focus on some features in the correlations patterns, in particular of density-density correlations. The application to the study of the Hawking signal in the formation of acoustic black hole-like configurations is also discussed.
We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quench…
We measure the correlation spectrum of the Hawking radiation emitted by an analogue black hole and find it to be thermal at the Hawking temperature implied by the analogue surface gravity. The Hawking radiation is in the regime of linear dispersion, in analogy with a real black hole. Furthermore, the radiation inside of the black hole is seen to be composed of negative-energy partners only. This work confirms the prediction of Hawking's theory regarding the value of the Hawking temperature, as well as the thermality of the spectrum. The thermality of Hawking radiation is the root of the inform…
Inspired by a recent experiment by Steinhauer and co-workers, we present a simple model which describes the formation of an acoustic black hole in a Bose-Einstein condensate, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. We show the emergence of analog Hawking radiation out of a "quantum atmosphere" region significantly displaced from the horizon. This is quantitatively studied both at $T=0$ and even in the presence of an initial temperature T, as is always the case experimentally.
We obtain the analytic solutions of the radial part of the massless Klein-Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. From these solutions, we obtain the scalar waves near the acoustic horizon. We discuss the analogue Hawking radiation of massless scalar particles and the features of the spectrum associated with the radiation emitted by these acoustic black holes.
We show that spherical accretion onto astrophysical black holes can be considered as a natural example of analogue system. We provide, for the first time, an exact analytical scheme for calculating the analogue Hawking temperature and surface gravity for general relativistic accretion onto astrophysical black holes. Our calculation may bridge the gap between the theory of transonic astrophysical accretion and the theory of analogue Hawking radiation. We show that the domination of the analogue Hawking temperature over the actual Hawking temperature may be a real astrophysical phenomena. We als…
These notes introduce the fundamentals of black hole geometry, the thermality of the vacuum, and the Hawking effect, in spacetime and its analogues. Stimulated emission of Hawking radiation, the trans-Planckian question, short wavelength dispersion, and white hole radiation in the setting of analogue models are also discussed. No prior knowledge of differential geometry, general relativity, or quantum field theory in curved spacetime is assumed.
We present a method for exploring analogue Hawking radiation using a laser pulse propagating through an underdense plasma. The propagating fields in the Hawking effect are local perturbations of the plasma density and laser amplitude. We derive the dependence of the resulting Hawking temperature on the dimensionless amplitude of the laser and the behaviour of the spot area of the laser at the analogue event horizon. We demonstrate one possible way of obtaining the analogue Hawking temperature in terms of the plasma wavelength, and our analysis shows that for a high intensity near-IR laser the …
This chapter is an introduction to the Bogoliubov theory of dilute Bose condensates as applied to the study of the spontaneous emission of phonons in a stationary condensate flowing at supersonic speeds. This emission process is a condensed-matter analog of Hawking radiation from astrophysical black holes but is derived here from a microscopic quantum theory of the condensate without any use of the analogy with gravitational systems. To facilitate physical understanding of the basic concepts, a simple one-dimensional geometry with a stepwise homogenous flow is considered which allows for a ful…
We study the quantum fluctuations in a one dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.
The density density correlation function is computed for the Bogoliubov pseudoparticles created in a Bose-Einstein condensate undergoing a black hole flow. On the basis of the gravitational analogy, the method used relies only on quantum field theory in curved spacetime techniques. A comparison with the results obtained by ab initio full condensed matter calculations is given, confirming the validity of the approximation used provided the profile of the flow varies smoothly on scales compared to the condensate healing length.
Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the ``surface gravity'') is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose--Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a …
We observe spontaneous Hawking radiation, stimulated by quantum vacuum fluctuations, emanating from an analogue black hole in an atomic Bose-Einstein condensate. Correlations are observed between the Hawking particles outside the black hole and the partner particles inside. These correlations indicate an approximately thermal distribution of Hawking radiation. We find that the high energy pairs are entangled, while the low energy pairs are not, within the reasonable assumption that excitations with different frequencies are not correlated. The entanglement verifies the quantum nature of the Ha…
The constant curvature (CC) black holes are higher dimensional generalizations of BTZ black holes. It is known that these black holes have the unusual topology of ${\cal M}_{D-1}\times S^1$, where $D$ is the spacetime dimension and ${\cal M}_{D-1}$ stands for a conformal Minkowski spacetime in $D-1$ dimensions. The unusual topology and time-dependence for the exterior of these black holes cause some difficulties to derive their thermodynamic quantities. In this work, by using globally embedding approach, we obtain the Hawking temperature of the CC black holes. We find that the Hawking temperat…
We model a sonic black hole analog in a quasi one-dimensional Bose-Einstein condensate, using a Gross-Pitaevskii equation matching the configuration of a recent experiment by Steinhauer [Nat. Phys. 10, 864 (2014)]. The model agrees well with important features of the experimental observations, demonstrating their hydrodynamic nature. We find that a zero-frequency bow wave is generated at the inner (white hole) horizon, which grows in proportion to the square of the background condensate density. The relative motion of the black and white hole horizons produces a Doppler shift of the bow wave a…
We propose the use of a superconducting waveguide formed from an array of dc-SQUID's for investigating analogue Hawking radiation. Biasing the array with a space-time varying flux modifies the propagation velocity of the waveguide, leading to an effective metric with an horizon. Being a fundamentally quantum mechanical device, this setup allows for investigations of quantum effects such as back-reaction and analogue space-time fluctuations on the Hawking process.
Stimulated emission by black holes is discussed in light of the analogue gravity program. We first consider initial quantum states containing a definite number of particles, and then we take into account the case where the initial state is a coherent state. The latter case is particularly significant in the case where Hawking radiation is studied in dielectric black holes, and the emission is stimulated by a laser probe. We are particularly interested in the case of the electromagnetic field, for which stimulated radiation is calculated too.
The sonic analogue of Hawking radiation can now be experimentally recreated in Bose-Einstein Condensates that contain an acoustic black hole. In these experiments the signal strength and analogue Hawking temperature increase for denser condensates, which however also suffer increased atom losses from inelastic collisions. To determine how these affect analogue Hawking radiation, we numerically simulate creation of the latter in a Bose-Einstein Condensate in the presence of atomic losses. In particular we explore modifications of density-density correlations through which the radiation has been…
Hawking radiation, despite being known to theoretical physics for nearly forty years, remains elusive and undetected. It also suffers, in its original context of gravitational black holes, from practical and conceptual difficulties. Of particular note is the trans-Planckian problem, which is concerned with the apparent origin of the radiation in absurdly high frequencies. In order to gain better theoretical understanding and, it is hoped, experimental verification of Hawking radiation, much study is being devoted to laboratory systems which use moving media to model the spacetime geometry of b…
We propose the use of a waveguide-like transmission line based on direct-current superconducting quantum interference devices (dc-SQUID) and study the sine-Gordon (SG) equation which characterises the dynamical behavior of the superconducting phase in this transmission line. Guided by the duality between black holes in Jackiw-Teitelboim (JT) dilaton gravity and solitons in sine-Gordon field theory, we show how to, in our setup, realize 1 + 1 dimensional black holes as solitons of the sine-Gordon equation. We also study the analogue Hawking radiation in terms of the quantum soliton evaporation,…
We analytically study the low-frequency properties of the analogue Hawking effect in Bose-Einstein condensates. We show that in one-dimensional flows displaying an analogue horizon, the Hawking effect is dominant in the low-frequency regime. This happens despite non vanishing greybody factors, that is, the coupling of the Hawking mode and its partner to the mode propagating with the flow. To show this, we obtained analytical expressions for the scattering coefficients, in general flows and taking into account the full Bogoliubov dispersion relation. We discuss the obtained expressions for the …
The observation of quantum Hawking radiation and its entanglement in an analogue black hole was recently reported. A subsequent note (arXiv:1609.03803) criticized the study. Version 2 of the note was recently presented. The note suffers from technical difficulties which invalidate its main claims. We answer all of the comments in the note and show that the criticisms are not valid. We also answer a comment made by the author of the note in a different forum.
The conversion of positive-frequency waves into negative-frequency waves at the event horizon is the mechanism at the heart of the Hawking radiation of black holes. In black-hole analogues, horizons are formed for waves propagating in a medium against the current when and where the flow exceeds the wave velocity. We report on the first direct observation of negative-frequency waves converted from positive-frequency waves in a moving medium. The measured degree of mode conversion is significantly higher than expected from theory.
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.
We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high energy tail of the distribution of Hawking radiation should be entangled, whereas the low energy par…
The condensates of cold atoms at zero temperature in the tunable binary Bose-Einstein condensate system are studied with the Rabi transition between atomic hyperfine states where the system can be represented by a coupled two-field model of gapless excitations and gapped excitations. We set up the configuration of the supersonic and subsonic regimes with the acoustic horizon between them in the elongated two-component Bose-Einstein condensates, trying to mimic Hawking radiations, in particular due to the gapped excitations. The simplified step-like sound speed change is adopted for the subsoni…
We consider further on the problem of the analogue Hawking radiation. We propose a fourth order ordinary differential equation, which allows to discuss the problem of Hawking radiation in analogue gravity in a unified way, encompassing fluids and dielectric media. In a suitable approximation, involving weak dispersive effects, WKB solutions are obtained far from the horizon (turning point), and furthermore an equation governing the behaviour near the horizon is derived, and a complete set of analytical solutions is obtained also near the horizon. The subluminal case of the original fluid model…
The Fourier transform of the density-density correlation function in a Bose-Einstein condensate (BEC) analog black hole is a useful tool to investigate correlations between the Hawking particles and their partners. It can be expressed in terms of $\langle ^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}\ ^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} \rangle$, where $^{\text{out}}\hat{a}_{\text{up}}^{\text{ext}}$ is the annihilation operator for the Hawking particle and $^{\text{out}}\hat{a}_{\text{up}}^{\text{int}} $ is the corresponding one for the partner. This basic quantity is calculated for …
Propagation of coherent light in a Kerr nonlinear medium can be mapped onto a flow of an equivalent fluid. Here we use this mapping to model the conditions in the vicinity of a rotating black hole as a Laguerre-Gauss vortex beam. We describe weak fluctuations of the phase and amplitude of the electric field by wave equations in curved space, with a metric that is similar to the Kerr metric. We find the positions of event horizons and ergoregion boundaries, and the conditions for the onset of superradiance, which are simultaneously the conditions for a resonance in the analogue Hawking radiatio…
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.
We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose condensed atoms. These setups contain at least one black hole sonic horizon from which the analog of Hawking radiation should be generated and emitted against the flow in the subsonic region. Multiple coherent scattering by the double-barrier structure strongly modulates the transmission probability of phonons, rendering it very sensitive to their frequency. As a result, resonant tunneling occurs with high probability within a few narrow frequency intervals. This gives rise to highly no…
Hawking radiation, the spontaneous emission of thermal photons from an event horizon, is one of the most intriguing and elusive predictions of field theory in curved spacetimes. A formally analogue phenomenon occurs at the supersonic transition of a fluid: in this respect, ultracold gases stand out among the most promising systems but the theoretical modelling of this effect has always been carried out in semiclassical approximation, borrowing part of the analysis from the gravitational analogy. Here we discuss the exact solution of a one-dimensional Bose gas flowing against an obstacle, showi…
We construct quantum field theory in an analogue curved spacetime in Bose-Einstein condensates based on the Bogoliubov-de Gennes equations, by exactly relating quantum particles in curved spacetime with Bogoliubov quasiparticle excitations in Bose-Einstein condensates. Here, we derive a simple formula relating the two, which can be used to calculate the particle creation spectrum by solving the time-dependent Bogoliubov-de Gennes equations. Using our formulation, we numerically investigate particle creation in an analogue expanding Universe which can be expressed as Bogoliubov quasiparticles i…
Hawking radiation was originally proposed in astrophysics, but it has been generalized and extended to other physical systems receiving the name of analogue Hawking radiation. In the last two decades, several attempts have been made to measure it in a laboratory, one of the most successful systems is in optics. Light interacting in a dielectric material causes an analogue Hawking effect, in fact, its stimulated version has already been detected and the search for the spontaneous signal is currently ongoing. We briefly review the general derivation of Hawking radiation, then we focus on the opt…
We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irr…
Our knowledge of dynamical black holes suffers from a lack of observational insight. In an analogue model of gravity, we can design a longitudinally symmetric dynamical acoustic black hole with a moving horizon. In this symmetric spacetime, the marginally outer trapped surface and the so called evolving horizon are degenerate. Interestingly, there are many ways of assigning a surface gravity to the horizon in the absence of time translation invariance. Here, we present two of them that are distinguished by whether they are defined only locally or take into account the global properties of spac…
We use the identification of the edge mode of the filling fraction $ν=1$ quantum Hall phase with a 1+1 dimensional chiral Dirac fermion to construct an analogue model for a chiral fermion in a space-time geometry possessing an event horizon. By solving the model in the lowest Landau level, we show that the event horizon emits particles and holes with a thermal spectrum. Each emitted quasiparticle is correlated with an opposite-energy partner on the other side of the event horizon. Once we trace out these "unobservable" partners, we are left with a thermal density matrix.
