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 three different models for the BEC flow. It is shown that in each model the inclusion of the effective potential in the mode equations makes a significant difference. Furthermore, particle production induced by this effective potential in the interior of the black hole is studied for each model and shown to be nonthermal. An interesting peak that is related to the particle production and is present in some models is discussed.
We outline the derivation of the Hawking quanta-partner signal in correlations, and highlight the specific application to detect it in density-density correlations in BECs.
In the information loss problem in black hole evaporation, investigation of the purification partner of a Hawking particle is crucial. It is a well-known fact that 3+1 dimensional spherically symmetric gravitational collapse can be approximately described by 1+1 dimensional moving mirror models. Since a detected particle in field theory is defined by what a particle detector observes, the diversity of detector designs yields a variety of particles and their partners. We provide a formula of generalized partners of detected particles emitted out of mirrors in arbitrary motion in a free massless…
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…
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…
The observation of the Hawking effect from black holes in the astrophysical context is unlikely. However, the analog of this effect is present in condensed matter systems. We focus on Bose-Einstein condensates, and on a proposal to detect it through correlation measurements.
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 consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.
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.
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 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.
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.
It has been proposed that a black hole horizon should generate Hawking radiation. In order to test this theory, we have created a narrow, low density, very low temperature atomic Bose-Einstein condensate, containing an analog black hole horizon and an inner horizon, as in a charged black hole. We observe Hawking radiation emitted by the black hole. This is the output of the black hole laser. We also observe the exponential growth of a standing wave between the horizons. The latter results from interference between the negative energy partners of the Hawking radiation and the negative energy pa…
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…
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 investigate, within the framework of Quantum Field Theory in curved space, the correlations across the horizon of a black hole in order to highlight the particle-partner pair creation mechanism at the origin of Hawking radiation. The analysis concerns both acoustic black holes, formed by Bose-Einstein condensates, and gravitational black holes. More precisely, we have considered a typical acoustic black hole metric with two asymptotic homogeneous regions and the Schwarzschild metric as describing a gravitational black hole. By considering equal time correlation functions, we find a striking…
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 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…
Momentum correlations of the Hawking effect in a quantum fluid
Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France（卡斯勒-布罗塞尔实验室，索邦大学，法国国家科学研究中心，巴黎高等师范学院-巴黎文理研究大学，法兰西公学院）；Instituto de Física, Universidade Federal Fluminense（物理研究所，弗鲁米嫩塞联邦大学）
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…
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…
Squeezed quantum states and partner modes in the moving mirror model of black hole evaporation
Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（国立台湾大学梁式科学宇宙学与粒子天体物理学中心）；Department of Physics and Center for Theoretical Sciences, National Taiwan University（国立台湾大学物理系与理论科学中心）；Graduate Institute of Astrophysics, National Taiwan University（国立台湾大学天文研究所）；Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University（斯坦福大学SLAC国家加速器实验室卡弗里粒子天体物理学与宇宙学研究所）；Physics Department & Energetic Cosmos Laboratory, Nazarbayev University（纳扎尔巴耶夫大学物理系与活力宇宙实验室）；Beyond Center for Fundamental Concepts in Science, Arizona State University（亚利桑那州立大学超越基础科学概念中心）；Department of Physics, Nagoya University（名古屋大学物理系）；Kansai Institute for Photon Science (KPSI), National Institute for Quantum Science and Technology (QST)（日本量子科学技术研究院光子科学关西研究所）
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…
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…
Bogoliubov pseudoparticle creation in a BEC undergoing a WH like flow is investigated analytically in the case of a one dimensional geometry with stepwise homogeneous regions. Comparison of the results with those corresponding to a BH flow is performed. The implications for the analogous gravitational problem is discussed.
In the context of analog gravity the Hawking effect can be generalized to domains outside astrophysics. Arguably, the most successful systems for this analogy have been so far the sonic and the optical ones. However, problems arise in the analog systems as their dispersive effects are too large to be ignored, and this in turn modifies the usual thermal spectrum of Hawking radiation. In this work we perform analytical and numerical studies on how the velocity profile modifies the Hawking temperature in dispersive media, including some with direct experimental application.
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 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.
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 …
We consider simple models of Bose-Einstein condensates to study analog pair-creation effects, namely the Hawking effect from acoustic black holes and the dynamical Casimir effect in rapidly time-dependent backgrounds. We also focus on a proposal by Cornell to amplify the Hawking signal in density-density correlators by reducing the atoms' interactions shortly before measurements are made.
High frequency dispersion does not alter the low frequency spectrum of Hawking radiation from a single black hole horizon, whether the dispersion entails subluminal or superluminal group velocities. We show here that in the presence of an inner horizon as well as an outer horizon the superluminal case differs dramatically however. The negative energy partners of Hawking quanta return to the outer horizon and stimulate more Hawking radiation if the field is bosonic or suppress it if the field is fermionic. This process leads to exponential growth or damping of the radiated flux and correlations…
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.
Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the…
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 aim of this letter is to clarify the relationships between Hawking radiation and the scattering of light by matter falling into a black hole. To this end we analyze the S-matrix elements of a model composed of a massive infalling particle (described by a quantized field) and the radiation field. These fields are coupled by current-current interactions and propagate in the Schwarzschild geometry. As long as the photons energy is much smaller than the mass of the infalling particle, one recovers Hawking radiation since our S-matrix elements identically reproduce the Bogoliubov coefficients o…
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.
This work introduces a synergistic combination of analytical methods and numerical simulations to study the propagation of weak wave-packet modes in an optical medium containing the analog of a pair white-black hole. We apply our tools to analyze several aspects of the evolution, such as (i) the region of the parameter space where the analogy with the Hawking effect is on firm ground and (ii) the influence that ambient thermal noise and detector inefficiencies have on the observability of the Hawking effect. We find that aspects of the Hawking effect that are of quantum origin, such as quantum…
The effect of the Hawking temperature on the entanglement and teleportation for the scalar field in a most general, static and asymptotically flat black hole with spherical symmetry has been investigated. It is shown that the same "initial entanglement" for the state parameter $α$ and its "normalized partners" $\sqrt{1-α^{2}}$ will be degraded by the Hawking effect with increasing Hawking temperature along two different trajectories except for the maximally entangled state. In the infinite Hawking temperature limit, corresponding to the case of the black hole evaporating completely, the state …
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.
Motivated by recent experimental efforts, we study a black hole analog induced by the propagation of a strong laser pulse in a nonlinear dielectric medium. Based on the Hopfield model (one pair of Sellmeier coefficients), we perform an analytic and fully relativistic microscopic derivation of the analog of Hawking radiation in this setup. The Hawking temperature is determined by the analog of the surface gravity (as expected), but we also find a frequency-dependent gray-body factor (i.e., a nonthermal spectrum at infinity) due to the breaking of conformal invariance in this setup.
