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We observe a thermal distribution of Hawking radiation, stimulated by quantum
vacuum fluctuations, emanating from an analogue black hole. This confirms
Hawking's prediction regarding black hole thermodynamics. The thermal
distribution is accompanied by correlations between the Hawking particles
outside the black hole and the partner particles inside. We find that the high
energy pairs of Hawking and partner particles are entangled, while the low
energy pairs are not. This has implications for the problem of information loss
in a black hole. The observation of Hawking radiation reported here verifies
Hawking's semiclassical calculation, which is viewed as a milestone in the
quest for quantum gravity.

To read the full-text of this research,

you can request a copy directly from the author.

... • Holographic entanglement entropy in optical systems: Using engineered optical systems, we can create analogs of holographic spacetimes and measure the entanglement entropy of subsystems. The predicted scaling of entanglement entropy with subsystem size provides a test of our framework [249]. ...

... A quantum information-theoretic approach to cosmology, relating cosmic evolution to the growth of quantum complexity [263]. 6. Proposals for experimental tests of the framework in cosmology [15], high-energy physics [12], and analogue gravity systems [249]. ...

... 4. The development of experimental protocols to test the predictions of holographic quantum gravity in table-top quantum systems and cosmological observations [249]. ...

This paper presents a comprehensive framework for extending holographic principles beyond AdS/CFT to general spacetimes. By incorporating quantum information measures such as entanglement entropy and complexity into modified Einstein field equations, we develop a Universal Holographic Principle applicable to diverse geometries, including flat spacetime, de Sitter space, and cosmological scenarios. This formalism yields generalized holographic entanglement entropy formulas, explores innovative bulk reconstruction techniques, and establishes profound connections between quantum information and spacetime geometry. Key contributions include a covariant formulation of holographic principles, applications to black hole thermodynamics and cosmology, and potential resolutions to longstanding issues in quantum gravity, such as the black hole information paradox and the problem of time. We derive modified Friedmann equations incorporating quantum effects, propose quantum corrections to inflationary observables, and suggest a holographic interpretation of dark energy. The framework offers new perspectives on the emergence of spacetime from quantum entanglement and the nature of time as complexity growth. We discuss promising experimental avenues for testing the theory in cosmological observations, high-energy physics, and analog gravity systems, while exploring connections to other approaches such as loop quantum gravity and causal set theory. This work contributes to a more unified understanding of quantum gravity across various spacetime geometries.

... Moreover, a characteristic signature of the occurrence of spontaneous emission, sometimes referred to as the Hawking moustache, is found in the two-point correlations between density fluctuations propagating on opposite sides of the horizon [16][17][18]. This observable is robust against finite temperature effects [17] and has been exploited to claim the first experimental observation of the Hawking effect in a single component condensate [19][20][21]. So far, the Hawking emission has escaped observation in any other analog system. ...

... Configurations involving a smoother horizon or inhomogeneous density profiles, which reproduce more closely the experimental conditions [19], have also been considered in the theoretical literature (see, for instance, [15,18]): the general features of the Hawking signal are qualitatively identical to the simplest discontinuous case (8) and the Hawking temperature recovers the prediction of the hydrodynamical approximation. ...

... As a first point, the toy model of Fig. 1 is one-dimensional (1D). While Bose-Einstein condensation is, strictly speaking, not possible in one spatial dimension, finite size effects allow to work with quasi-1D cigar-shaped condensates in which the transverse degrees of freedom are frozen [14,19,29]. In the case of two-component BECs, the spin degree of freedom can be effectively 1D without the need of reaching this one-dimensional regime. ...

We theoretically study stimulated and spontaneous Hawking emission from an analog horizon for spin modes in a two-component Bose-Einstein condensate, both with and without a coherent coupling between the two components. We highlight the conceptual and practical advantages that these systems offer to the experimental observation of the phenomenon, namely the massive nature of elementary excitations and the experimental accessibility of the different quadratures of the spin excitations. In particular, we go beyond the relativistic regimes previously addressed in the literature, and identify various observables that show a signature of the Hawking process, as well as additional features associated with the massive nature of the modes, such as undulations. Semi-analytical calculations of the scattering properties of the horizon and of two-point correlation functions of the emitted radiation in an ideal stationary setup are supported by time-dependent numerical simulations based on Gross-Pitaevskii and Bogoliubov theory.

... There are many analogue systems currently under study, in several of which the analogue Hawking effect has been experimentally observed (e.g., surface waves on flowing water [9], phonons in an atomic condensate [10], and photons in a varying-index optical fiber [11]). While the gravitational analogy is independent of the underlying dynamics responsible for the determination of the background [1][2][3][4][5][6][7], any experimentalist in Analogue Gravity has to cope with the many dynamical regimes of the probed condensed matter systems before selecting the best ones that will mimic the original astrophysical system. ...

... For example, while in hydrodynamics a flow profile is generated by having a fixed obstacle in an open channel with a flowing fluid pushed by an externally-driven pump [9], we might also consider moving the obstacle at constant speed in an initially static water column. The latter case is directly analogous to cold atom systems with a LASER step moving relative to the trapping well along the condensate [10]: in the absence of any other constraints, the two situations would be equivalent according to the principle of relativity. In practice, however, these cases are not equivalent as the flows do not actually extend to infinity, and so boundary conditions at the ends of the flow may need to be taken into account: the water may have an initial static depth, and/or a downstream gate may affect the dynamical water depth for a given flow rate. ...

... The vertical size of the obstacle (or the LASER step height in the analogous BEC experiments [10]) was considered as a relevant additional parameter and was subsequently adimensionalized in previous theoretical studies so as to classify flow regimes. In hydraulics, theoreticians have introduced the obstruction factor, namely the ratio between the maximum height of the obstacle to the upstream water depth [15,16]. ...

Accelerating/decelerating trans-critical flows (waterfalls/cataracts) are analogous to space-times of black holes/white fountains since the pioneering work of Sch{\"u}tzhold \& Unruh in 2002. A single number is usually employed to classify trans-criticality namely the local depth Froude number which is the ratio between the local current speed and the local celerity of long gravity waves analogous to the light celerity. When the former reaches one, water waves are no more able to propagate upstream: the hydraulic black hole is a river of no return for them. At a higher level of understanding, two global dimensionless numbers, the upstream Froude number F r up and the obstruction ratio r up (the height of a bottom obstacle, the underlying geometry inducing the effective space-time, divided by the upstream water depth) are essential to distinguish subcritical, trans-critical and supercritical zones in the -F r up versus r up -hydraulic and nondispersive diagram. The relationship between both global parameters for transcritical flows turns out to be a peculiar limit of the behaviour of boats navigating in confined media like canals or locks with a generalized obstruction factor based on the ratio between the boat section and the canal section. Here, we revisit the classification of flows over obstacles in open water channel taking into account both effects of dispersion and scale, two neglected topics so far. For the first time, we give a complete classification of flows in an open water channel based on sub-pixel detection method measurements of the free surface supported by numerical simulations. We generalized the obstruction factor by a filling factor taking into account the maximum height of the water channel, a crucial parameter that was overlooked so far. Our ultimate purpose is to understand how to reproduce in the laboratory analogues of curved space-times from the dynamical point of view.

... This can provide an interesting experimental test of the foundational effects predicted for QFTs in curved spacetimes, and actually provide useful information to guide our understanding of interacting regimes that are beyond the reach of traditional theoretical tools. Among other results, these analog simulators have successfully observed the Hawking radiation of bosonic fields using light propagation in non-linear media [11][12][13], and sound waves in Bose-Einstein condensates [14][15][16][17]. The Unruh effect and particle production in expanding universes have also been experimentally tested with ultracold atoms, trapped ions, and microcavity polaritons [18][19][20][21][22][23][24][25][26]. ...

... In our model, due to the block diagonal form of the Hamiltonian (16), each mode can be treated as an effective twolevel system, where the role of the time-dependent detuning in the two level system is given by ma(η) = −m/(Hη). In the free case, every mode is independent of the others, allowing for particle production to be calculated for each one independently. ...

... Therefore, when interactions are switched on, one can no longer solve the RTE for each mode independently. Nonetheless, one can still solve the RTE equations to find the specific evolution of the condensates in conformal time, and then plug them back into the self-consistent Hamiltonian (16). This allows to treat the condensates as effective parameters that lead to a specific change of the time dependence. ...

The phenomenon of particle production for quantum field theories in curved spacetimes is crucial to understand the large-scale structure of a universe from an inflationary epoch. In contrast to the free and fixed-background case, the production of particles with strong interactions and back reaction is not completely understood, especially in situations that require going beyond perturbation theory. In this work, we present advances in this direction by focusing on a self-interacting field theory of Dirac fermions in an expanding Friedmann-Robertson-Walker universe. By using a Hamiltonian lattice regularization with continuous conformal time and rescaled fields, this model becomes amenable to either a cold-atom analogue-gravity quantum simulation, or a dynamical variational approach. Leveraging a family of variational fermionic Gaussian states, we investigate how dynamical mass generation and the formation of fermion condensates associated to certain broken symmetries modify some well-known results of the free field theory. In particular, we study how the non-perturbative condensates arise and, more importantly, how their real-time evolution has an impact on particle production. Depending on the Hubble expansion rate, we find an interesting interplay of interactions and particle production, including a non-trivial back reaction on the condensates and a parity-breaking spectrum of produced particles.

... 1. Acoustic Black Holes: By creating regions of supersonic flow in a BEC, one can form acoustic event horizons that share many properties with gravitational black holes [64]. These systems could potentially be used to study the growth of complexity in black holelike settings. ...

... 4. Potential experimental avenues for testing holographic complexity ideas, including analog gravity systems [64] and gravitational wave observations [1]. While these experiments face significant challenges, they offer promising directions for bringing quantum gravity effects into the realm of observable phenomena [23]. ...

... 4. Pursuing experimental realizations of holographic systems in analog gravity and quantum computing platforms [64,58]. These experiments, while challenging, could provide valuable insights into the dynamics of complexity and its relation to spacetime geometry. ...

This paper explores the profound implications of the holographic bound on complexity growth, establishing a direct link between quantum information theory and the geometry of spacetime. By examining the relationship between quantum complexity and spacetime structure, it proposes a novel framework for understanding the emergence of gravity from quantum information. The paper investigates how this connection could lead to a more complete theory of quantum gravity, potentially resolving long-standing issues in theoretical physics such as the black hole information paradox and the unification of quantum mechanics with general relativity. It presents detailed mathematical derivations of key concepts including the Complexity-Volume (CV) and Complexity-Action (CA) dualities, and explores their implications for black hole physics and the emergence of classical spacetime. The paper also discusses potential experimental avenues for testing these ideas, including analog gravity systems, quantum computing, and gravitational wave observations. Finally, it outlines future research directions and challenges in extending these concepts to more general spacetime geometries and in reconciling them with other approaches to quantum gravity. Overall, this work offers a comprehensive exploration of how the holographic bound on complexity growth could provide new insights into the fundamental nature of spacetime, gravity, and quantum information.

... The (1 + 1)-dimensional effect has also been realized with trapped ions [55] and an optical system [56]. Outside the cosmological context, cold atoms were also used in theoretical and experimental studies of Hawking radiation [57][58][59][60][61], the Casimir effect [62], Unruh radiation [63][64][65] and false vacuum decay [66,67]. Furthermore, new simulation platforms to simulate kinematics of fermionic fields in curved spacetime have been proposed [68,69]. ...

... At a s,ref = 50 a 0 (where a 0 is the Bohr radius), a realistic value is c s,ref = 1.1µm/ms. With these values, the analogue Hubble parameter for the hallmark scenarios can be calculated: Consider first the power-law expansion (59). At initial time t i , eq. (A1) evaluates to ...

... = a s (t i ) is the scattering length at initial time. Introducing the final value a min s = a s (t i + ∆t), we can combine eqs.(59) and ( ...

The production of quantum field excitations or particles in cosmological spacetimes is a hallmark prediction of curved quantum field theory. The generation of cosmological perturbations from quantum fluctuations in the early universe constitutes an important application. The problem can be quantum-simulated in terms of structure formation in an interacting Bose-Einstein condensate (BEC) with time-dependent s-wave scattering length. Here, we explore a mapping between cosmological particle production in general (D+1)-dimensional spacetimes and scattering problems described by the non-relativistic stationary Schr\"odinger equation in one dimension. Through this mapping, intuitive explanations for emergent spatial structures in both the BEC and the cosmological system can be obtained for a large class of analogue cosmological scenarios, ranging from power-law expansions to periodic modulations. The investigated cosmologies and their scattering analogues are tuned to be implemented in a (2+1)-dimensional quantum field simulator.

... Black holes (BHs) are perfect playgrounds for quantum mechanics and general relativity given their understanding requires both [1]. Present quantum technologies provide accurately controllable platforms where analogue (sonic) BHs [2] can be realized [3][4][5][6] and investigated in one-to-one correspondence with precise theoretical predictions. The latter have the advantage that can be based either on quantum fluid-dynamics, just hinging on very general conservation laws and symmetries [7][8][9][10], or on microscopic theories of interacting matter based on accurately known microscopic Hamiltonians [11]. ...

... A number of BHs concepts have been investigated within an analogue-gravity approach, especially regarding the observation of Hawking radiation and temperature [2,3,6,12], all supporting the universal nature of the corresponding ideas. One of the most striking predictions of universal behavior concerns the shear viscosity-to-entropy density ratio η/s, that is conjectured to satisfy the so-called KSS bound η/s ⩾ 1/4π. ...

... Quantum fluctuations at the acoustic horizon result in a thermal radiation of phonons [7,[29][30][31][32][33][34] the sonic analogue of the Hawking radiation [1]. Noticeably, this emission of long-wavelength sonic vibrations at the acoustic horizon has been confirmed both numerically [9] and in the laboratory [3,5] with atomic Bose-Einstein condensates. ...

A transonic fluid flow generates an acoustic hole that is the hydrodynamic analogue of a gravitational black hole (BH). Acoustic holes emit a detectable thermal radiation of phonons at a characteristic Hawking temperature. The crucial concept is that the spontaneous phonon emission at the horizon produces an irreversible heat increase at the expenses of the bulk fluid kinetic energy. We show that such process can be described in terms of effective shear and bulk viscosities that are defined close to the horizon. We analyze this quantum friction process by resorting to a general kinetic theory approach as well as by the specific description of phonon emission as a tunneling process. The celebrated Kovtun, Son and Starinets (KSS) universal lower bound η/s=1/4π of the shear viscosity coefficient to entropy density ratio, readily follows, and is extended to the longitudinal bulk viscosity at the horizon. We come to the same saturation of the KSS bound after considering the shear viscosity arising from a perturbation of the background metric at the acoustic horizon providing a—in principle testable—realization of the so called BH membrane paradigm.

... • Holographic entanglement entropy in optical systems: Using engineered optical systems, we can create analogs of holographic spacetimes and measure the entanglement entropy of subsystems. The predicted scaling of entanglement entropy with subsystem size provides a test of our framework [132]. ...

... 3. Applications of the universal holographic principle to various spacetimes, including flat space [33], de Sitter space [134], black holes [5], and cosmological scenarios [20]. 4. Proposals for experimental tests of the framework in cosmology [11], high-energy physics [9], and analogue gravity systems [132]. 5. Connections to other approaches to quantum gravity, including loop quantum gravity [123], causal set theory [128], and string theory [149]. ...

This paper presents a comprehensive framework for extending holographic principles beyond AdS/CFT to general spacetimes. By incorporating quantum information measures such as entanglement entropy and complexity into modified Einstein field equations, we develop a Universal Holographic Principle applicable to diverse geometries, including flat spacetime, de Sitter space, and cosmological scenarios. This formalism derives generalized holographic entanglement entropy formulas, explores innovative bulk reconstruction techniques, and establishes profound connections between quantum information and spacetime geometry. Key contributions include a covariant formulation of holographic principles, applications to black hole thermodynamics and cosmology, and potential resolutions to longstanding issues in quantum gravity. We discuss promising experimental avenues for testing the theory in cosmological observations, high-energy physics, and analog gravity systems, while exploring connections to other approaches such as loop quantum gravity and causal set theory. This framework contributes to a more unified understanding of quantum gravity across various spacetime geometries.

... The boundary of the sisytube torus is at: (22) which occurs where: (23) In the uncharged Kerr geometry, the sisytube is entirely at negative radius, r < 0, but in the Kerr-Newman geometry the sisytube extends to positive radius, Figure 1. ...

... (www.preprints.org) | NOT PEER-REVIEWED | Posted: 2 August 2024 doi:10.20944/preprints202408.0101.v123 ...

Here we will explain the correlation between the Kerr-Newman diagram and the theory: RLC electrical modelling of a black hole and the early universe. We will develop a black hole model that describes and explains both theories. In the development of our analysis, we will emphasize the following conditions: M² > Q² + a², M² = Q² + a² and M² < Q² + a² and we will also analyse the condition in which the mass of a black hole reaches its critical mass M = Mc. We will demonstrate that the interpretation of the Kerr-Newman diagram is equivalent to the interpretation of the theory: RLC electrical modelling of a black hole and the early universe. Finally, we will generalize the proposed model for a black hole and propose a black hole model formed by negative particles, neutroniumd, which after reaching critical conditions of mass, pressure, volume, temperature, density, etc.; decays into a positively charged black hole, protoniu. Let us remember that both models are formed by charged particles of matter (they do not contain antimatter), but their vector configuration means that the net charges of both proposed black holes are zero.

... where ϵ is a small parameter and ρ 0 is a reference computational density. While direct observation of Hawking radiation is currently beyond our technological capabilities, this prediction could be tested in analog black hole systems [24] or through indirect observations of primordial black holes [25]. ...

... • It suggests new avenues for exploring quantum gravity effects in analog systems or table-top experiments [24]. ...

Dr. Femi Oyewole presents a unified theoretical framework that integrates Andrew King's Unified Geometric Wave Theory (UGWT) with advanced concepts in quantum gravity, computational complexity, and cosmology. This paper synthesizes UGWT’s wave-centric approach with extended quantum state normalization in Banach spaces and computational density in cosmic structures. The comprehensive model bridges microscopic quantum phenomena with macroscopic cosmological processes, addressing fundamental questions in physics, such as the nature of quantum gravity, the origin of cosmic structure, and the evolution of the universe. Key contributions include a generalized wave equation in Banach spaces, an information-theoretic formulation of computational density, and quantum gravity field equations. The study proposes a dynamic dark energy model arising from nested universe structures and offers potential resolutions to issues like the black hole information paradox and cosmological singularities. Experimental tests and observational consequences are also proposed, spanning high-energy physics to cosmological observations.
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

... For the observation of spontaneous Hawking radiation, the power of the step potential is a constant (unlike the black curve of Fig. 1(a)), and the edge moves with a constant speed (the ramp of the red curve). The correlation plot of Fig. 2(a) shows the spontaneous Hawking radiation, which is similar to the previous observations [21][22][23], and to the predictions for real black holes [24][25][26]. ...

... The narrower band reflects the quantum origin of the spontaneous Hawking radiation, as opposed to the classical fluctuations which we have added artificially. The magnitude squared of the Fourier transform of the spontaneous band is proportional to the product of Bogoliubov coefficients (| | 2 [21,29]. This product is greater than | | 4 , which implies that the Hawking/partner pairs are entangled [30]. ...

Due to quantum gravity, a black hole horizon should feature quantum fluctuations. We explore the possibility that these fluctuations radiate Hawking radiation dynamically. By studying the observed ringdowns after black hole mergers, we find that the amplitude of the horizon fluctuations should be on the order of the Planck length, in order to emit the quantity of gravitons corresponding to Hawking radiation. If the horizon fluctuations themselves are quasinormal modes, then the Hawking graviton spectrum is much more accurate than the usual blackbody spectrum. Furthermore, it would only take one quasinormal mode, with its broad, damped spectrum, to emit the entire Hawking spectrum of gravitons. We check the dynamical Hawking radiation hypothesis by means of a sonic black hole; we induce additional fluctuations in the horizon, and observe enhanced Hawking radiation. As expected, we see that the spontaneous Hawking radiation is entangled, while the enhanced Hawking radiation is not, since we induce it deterministically.

... for the observation of negative-frequency waves at the event horizon [8,9], stimulated Hawking emission [10] classical Hawking correlations [11] and wave scattering processes [12]. Experiments in Bose-Einstein condensates (BECs) achieved the sensitivity to detect quantum correlations between outgoing and ingoing phonon pairs at the horizon [13], a key signature of the quantum nature of acoustic Hawking radiation. The measured correlation spectrum of phonon fluctuations in the vicinity of the horizon is thermal with a temperature given by the surface gravity [14] and the process occurs spontaneously [15], confirming the predictions of Hawking's theory. ...

... Hawking pairs at the horizon [13]. Advanced versions of these setups might soon be able to extract correlations between condensed atomic states (which, in the mean field limit, give rise to the global geometry), and their collective quantum excitations, thus paving the way for exploring the physics of event horizons which are purely quantum in nature. ...

Recent experimental progresses in controlling classical and quantum fluids have made it possible to realize acoustic analogues of gravitational black holes, where a flowing fluid provides an effective spacetime on which sound waves propagate, demonstrating Hawking-like radiation and Penrose superradiance. We propose the exciting possibility that new hydrodynamic systems might provide insights to help resolve mysteries associated with quantum gravity, including the black hole information-loss paradox and the removal of spacetime singularities.

... In order to study quantum effects of this type, access to a black hole is not mandatory. Many analog systems such as negative-frequency waves 9-12 , Bose-Einstein condensates 13 , optical fibers 14 , and shallow water waves 15 are experimentally accessible. While the focus of these works lies on the observation of effects similar to Hawking radiation, here we are interested in the measurement of its origin 8,16 , that is, of the logarithmic phase singularity in a mode function close to an event horizon. ...

... with the carrier frequency Ω 0 = 15 rad/s and the initial amplitude a 0 = 2 mm. Here A = A(t) and φ A = φ A (t) represent the amplitude and phase of the eigenfunctions obtained from Eqs. (13) and (14). For this purpose we make use of the substitutions as defined previously in order to translate quantummechanical variables to the formalism of surface gravity water waves. ...

In 1974, Stephen Hawking predicted that quantum effects in the proximity of a black hole lead to the emission of particles and black hole evaporation. At the very heart of this process lies a logarithmic phase singularity which leads to the Bose-Einstein statistics of Hawking radiation. An identical singularity appears in the elementary quantum system of the inverted harmonic oscillator. In this Letter we report the observation of the onset of this logarithmic phase singularity emerging at a horizon in phase space and giving rise to a Fermi-Dirac distribution. For this purpose, we utilize surface gravity water waves and freely propagate an appropriately tailored energy wave function of the inverted harmonic oscillator to reveal the phase space horizon and the intrinsic singularities. Due to the presence of an amplitude singularity in this system, the analogous quantities display a Fermi-Dirac rather than a Bose-Einstein distribution.

... The analogue gravity idea of Unruh has led to the first observations of phenomena related to the paradigmatic quantum Hawking effect in the experimentally realizable physical system Bose-Einstein condensate (BEC), an ultracold quantum gas of interacting bosons [18][19][20], the analogue gravity arena we focus on in the present study. Other BEC analogue gravity experiments have probed aspects of cosmology, such as Hubble friction and preheating [21], as well as phenomena related to cosmological particle production [22,23]. ...

We consider the number-conserving unitary dynamics of a Bose-Einstein condensates at absolute zero, and argue that an analogue gravity model in such a setting must take into account the backreaction of quasiparticle excitations onto the condensate background. This in turn requires that one expands to second order in perturbations, and takes the nonlinearity of the theory into account. It is shown that this leads to significant modifications of the standard linearized analogue gravity paradigm \`a la Unruh. In particular, to obtain a fully Lorentz-covariant equation in curved spacetime for second-order perturbations, we demonstrate that it is necessary to introduce, to leading order in powers of the formal expansion parameter $N^{-1/2}$ (where $N$ is total particle number), a quantum-fluctuation-renormalized spacetime metric which substantially differs from the Unruh metric and, to subleading order, two emergent vector fields. Both the renormalized metric and the vector fields then keep track of the effect of the backreaction of the quasiparticles onto the condensate up to the order in powers of $N^{-1/2}$ considered. Finally, we apply our formalism to an analogue-cosmological Friedmann-Lema\^{i}tre-Robertson-Walker metric and establish its renormalized form due to quantum many-body backreaction.

... For instance, peculiar long-range patterns of density-density correlation function have been predicted as evidence of Hawking radiation from sonic black holes in a flowing one-dimensional (1D) atomic Bose-Einstein condensate (BEC) [7]. Recently, both self-amplifying and spontaneous Hawking radiations of phonons were observed from such analogue black holes by measuring density-density correlation patterns [8,9]. ...

Density–density correlation analysis is a convenient diagnostic tool to reveal the hidden order in the strongly correlated phases of ultracold atoms. We report on a study of the density–density correlations of ultracold bosonic atoms which were initially prepared in a Mott insulator (MI) state in one-dimensional optical lattices. For the atomic gases released from the deep optical lattice, we extracted the normalized density–density correlation function from the atomic density distributions of freely expanded atomic clouds. Periodic bunching peaks were observed in the density–density correlation spectra, as in the case of higher-dimensional lattices. Treating the bosonic gas within each lattice well as a subcondensate without quantum tunneling, we simulated the post-expansion density distribution along the direction of the 1D lattice, and the calculated density–density correlation spectra agreed with our experimental observations.

... Like its gravitational counterpart, the salient feature of an acoustic black hole spacetime is the existence of a causal boundary, here called the acoustic horizon -a trapping outer surface that no outgoing null particles can escape [12,13], with sound modes taking the role of null particles instead of photons [11,12]. More than just a theoretical model, acoustic black holes have been produced in various experimental implementations, mostly for the purpose of laboratory simulations of Hawking radiation, black hole superradiance, and earth-bound searches for quantum gravity signatures [14][15][16][17]. Recent theoretical studies explored the case of acoustic black holes in fluids embedded in curved spacetime [18][19][20][21], and demonstrated that in general, information about the physical background spacetime must be encoded in the effective metric of acoustic gravity [18,19]. ...

The sound modes of a flowing superfluid is described by the massless Klein-Gordon equation in an effective background metric. This effective background metric can be designed to mimick a black hole using the acoustic horizon. In this work, we study the AdS/CFT dual of the sound modes in the presence of an acoustic horizon in the bulk. Focusing on fluids with a purely radial flow, we derive the metric tensor for the effective acoustic spacetime and deduce a necessary condition for an acoustic black hole geometry to exist within the fluid. Using specific examples of superfluid velocity profiles, we obtained the source, operator expectation value, Green's function, and spectral density of the dual field theory by solving for the asymptotic behavior of the sound modes near the AdS boundary. In all our examples, the sound modes remain gapless but the excitations are described by branch cuts, instead of poles, which is typical of strongly coupled systems. Furthermore, we calculate the effective Hawking temperature of the dual field theory associated with the bulk acoustic horizon. Lastly, we investigate the near horizon properties and derive the superfluid velocity profile that can give rise to an infrared emergent quantum criticality.

... As such, proof-of-principle experimental demonstration from the perspective of quantum simulation could be within reach. Representative paradigms include analogue Hawking radiation [12][13][14][15][16][17][18][19][20][21], cosmological particle production [22][23][24][25][26][27], and the dynamical Casimir effect [28][29][30][31][32]. Recently, degradation of quantum correlation due to the Unruh effect has been experimentally simulated [33,34]. In addition, Unruh radiation has been reported through Bose-Einstein condensate [35], where a dynamical two-mode squeezed quantum field is constructed and observed, in mathematically analogy to the field seen by the non-inertial observer. ...

The Unruh effect predicts an astonishing phenomenon that an accelerated detector would detect counts despite being in a quantum field vacuum in the rest frame. Since the required detector acceleration for its direct observation is prohibitively large, recent analog studies in quantum simulation platforms help in revealing various properties of the Unruh effect and thus to explore the not-yet-understood physics of quantum gravity. To further reveal the quantum aspect of the Unruh effect, analogous experimental exploration of the correlation with respect to the detector and the field, and the consequences for coherent quantum trajectories of the detector that without classical counterparts, are essential steps but currently missing. Here, we utilize a laser-controlled trapped ion to experimentally simulate an oscillating detector coupled with a cavity field. We observe joint excitation of both the detector and the field in the detector’s frame, matching with the coordinated dynamics predicted by the Unruh effect. Particularly, we simulate the detector moving in single and superposed quantum trajectories, where the latter case shows coherent interference of excitation. Our demonstration reveals properties of quantum coherent superposition of accelerating trajectories associated with quantum gravity theories that have no classical counterparts, and may offer a new avenue to investigate phenomena in quantum field theory and quantum gravity. We also show how a generalization of the method and results in this work may be beneficial for direct observation of the Unruh effect.

... In the case of acoustic black holes constructed from Bose-Einstein condensates, it has been predicted that the correlations between the Hawking particles and their partners will form a stationary peak in the equal time density-density correlator, which appears at late times after the formation of the sonic horizon, with one point taken inside it and the other outside [4], [5]. This striking feature has indeed been experimentally observed [6], [7] and it is the most stringent evidence of Hawking-like (phonons in this case) radiation in an analogue black hole. Inspired by these results, R. Balbinot and A. Fabbri [1] calculated the equal time density-density correlator of a massless scalar field on a Schwarzschild black hole background, finding a result which is in disagreement with the acoustic black hole case: the expected peak signaling the particle-partner correlations does not appear. ...

Hawking radiation can be regarded as a spontaneous and continuous creation of virtual particle-antiparticle pairs outside the event horizon of a black hole where strong tidal forces prevent the annihilation: the particle escapes to infinity contributing to the Hawking flux, while its corresponding antiparticle partner enters the event horizon and ultimately reaches the singularity. The aim of this paper is to investigate the energy density correlations between the Hawking particles and their partners across the event horizon of two models of non-singular black holes by calculating the two-point correlation function of the density operator of a massless scalar field. This analysis is motivated by the fact that in acoustic black holes particle-partner correlations are signalled by the presence of a peak in the equal time density-density correlator. Performing the calculation in a Schwarzschild black hole it was shown in [1] that the peak does not appear, mainly because of the singularity. It is then interesting to consider what happens when the singularity is not present. In the Hayward and Simpson-Visser non-singular black holes we show that the density-density correlator remains finite when the partner particle approaches the hypersurface that replaces the singularity, opening the possibility that partner-particle correlations can propagate towards other regions of spacetime instead of being lost in a singularity.

... One possible route for studying such small effects is offered by analogue gravity in Bose-Einstein condensates (BEC). This program, that gained momentum with [9], is welldeveloped [10], and counts with examples ranging from black hole to cosmological analogues [11][12][13][14][15]. Also, the analogue gravity community has achieved an impressive milestone: The measurement of an analogue Hawking radiation [16,17]. ...

Bose-Einstein condensates are suitable systems for studying fundamental aspects of quantum backreaction. Here the backreaction problem in 1D condensates is considered from the perspective of energy and momentum conservation. By assuming the validity of Bogoliubov theory, the backreaction equations are used to identify the contributions to the system energy and momentum coming from quantum fluctuations and condensate corrections. The backreaction is solved for a condensate trapped in a ring configuration and such that particle interactions are continuously switched on. It is shown that the energy in the condensate cannot be addressed without taking into account how the system entered the interacting regime, and even for homogeneous condensates the power transferred to the condensate by quantum fluctuations showcases an intricate non-monotonic pattern.

... Alternatively, Leonhardt 14 argued that, if an ultrashort pulsed UV laser is injected into a dielectric fiber to drive the medium to move at high speeds, the desirable Hawking radiation can occur in the vicinity of the velocity-domain optical system, wherein the propagation of infrared light through the fiber can be faster than the velocity of the medium's motion. In particular, the critical behavior of the acoustic wave propagation in BEC systems had also been utilized to construct the analogue black hole 15,16 , whose Hawking radiation can be detected by measuring the density correlation function of the BEC particles on both sides of its acoustic horizon, when the flow rate of the BEC particles exceeds its mid-acoustic propagation velocity. The measured Hawking radiation temperature is on the order of 10 −10 K. Inspired by these pioneering experiments for analogue Hawking radiation detection, more gravity-like black holes are expected to be constructed to confirm the existence of analogues of Hawking radiation. ...

Given that the Hawking radiation from celestial black holes is extremely weak and thus difficult to be detected practically, a series of analogue black holes have been constructed to observe the relevant analogue Hawking radiations in the laboratory. In this paper, based on the critical behavior of group velocity of the microwave signal propagating along a controllable composite right/left-handed transmission line, we theoretically demonstrate that an electromagnetic black hole can be constructed in the co-moving coordinate system; in the velocity space, its horizon is at the point, where the electromagnetic wave propagation group velocity equals to the propagation velocity of the voltage solitary wave. With the typical experimental parameters, the Hawking radiation temperature of such an electromagnetic black hole can be estimated as ∼ 30mK, and thus the radiation could be detected, in principle, by the current low-temperature experimental technique.

... Unfortunately, due to the considerable energy scales and the extreme conditions necessary to witness such phenomena, their direct observation has not been possible to date. Nevertheless, in the last decade, impressive advancements in quantum technologies based on quantum simulation platforms have led to the successful fabrication of devices that mimic well the main features of such highly energetic phenomena [16][17][18][19][20][21]. ...

Transmission lines (TLs) are excellent examples of quantum simulators of quantum fields. By appropriately driving-specific circuit elements, these devices can reproduce relativistic and quantum phenomena such as particle creation due to the nonadiabatic stimulation of the quantum vacuum. We investigate particle creation in left-handed TLs induced by the modulation of the Josephson energy in superconducting quantum interference devices. Our results show that, as a consequence of the peculiar dispersion relations present in these systems, particle production occurs with much more favorable conditions with respect to the usual right-handed TLs.
Published by the American Physical Society 2024

... Analogies in physics are powerful tools that allow us to explore cosmological phenomena using more accessible or experimentally feasible systems. For example, Bose-Einstein condensates are used to create analogies for studying spontaneous Hawking radiation [15]. Such analogies are common and invaluable for realizing and understanding physical systems through the behavior of other systems. ...

We follow the assumption that relativistic causality is a key element in the structure of quantum mechanics and integrate the speed of light, c, into quantum mechanics through the postulate that the (reduced) Planck constant is a function of c with a leading order of the form ℏc∼Λ/cp for a constant Λ>0, and p>1. We show how the limit c→∞ implies classicality in quantum mechanics and explain why p has to be larger than 1. As the limit c→∞ breaks down both relativity theory and quantum mechanics, as followed by the proposed model, it can then be understood through similar conceptual physical laws. We further show how the position-dependent speed of light gives rise to an effective curved space in quantum systems and show that a stronger gravitational field implies higher quantum uncertainties, followed by the varied c. We then discuss possible ways to find experimental evidence of the proposed model using set-ups to test the varying speed of light models and examine analogies of the model based on electrons in semiconductor heterostructures.

... As such, physicists have started to explore a variety of quantum systems in which the underlying metric could be controlled in laboratories. For instance, acoustic black holes and tunable curvatures have been realized for phonons in Bose-Einstein condensates [6][7][8][9][10][11][12][13][14][15][16]. In parallel, superconducting and electric circuits may be used to realize certain tiling of hyperbolic surfaces [17][18][19][20], and photonic devices have been engineered to study general relativity [21][22][23][24][25][26][27][28]. ...

Quantum matter in curved spaces exhibits remarkable properties unattainable in flat spaces. To access curved spaces in laboratories, the conventional wisdom is that physical distortions need to be implemented into a system. In contrast to this belief, here, we show that two hyperbolic surfaces readily exist in bosonic Kitaev model in the absence of any physical distortions and give rise to a range of intriguing phenomena, such as chiral quantum transport or chiral reaction-diffusion. A finite chemical potential couples these two hyperbolic surfaces, delivering a quantum sensor whose sensitivity grows exponentially with the size of the system. Our results provide experimentalists with an unprecedented opportunity to explore intriguing quantum phenomena in curve spaces without distortion or access non-Hermitian phenomena without dissipation. Our work also suggests a new class of quantum sensors in which geometry amplifies small signals.

... This field can also stimulate novel understanding by bringing ideas from curved spacetime quantum field theory into condensed-matter and coldatom settings. Some of the analog gravity platforms that have been studied include proposals to simulate black holes and Hawking Radiation [5][6][7][8], the properties of the expanding universe such as inflation [9][10][11][12][13][14][15][16] and curvature [17][18][19], and other phenomena such as the dynamical Casimir effect [20], Sakharov oscillations [21], and rotational superradiance [22]. ...

We study one-dimensional Dirac fermions in the presence of a spatially-varying Dirac velocity $v(x)$, that can form an approximate lab-based Rindler Hamiltonian describing an observer accelerating in Minkowski spacetime. A sudden switch from a spatially homogeneous velocity ($v(x)$ constant) to a spatially-verying velocity ($v(x)$ inhomogeneous) leads to the phenomenon of particle creation, i.e., an analog Unruh effect. We study the dependence of the analog Unruh effect on the precise form of the velocity profile, finding that while the ideal Unruh effect occurs for $v(x) \propto |x|$, a modified Unruh effect still occurs for more realistic velocity profiles that are linear for $|x|$ smaller than a length scale $\lambda$ and constant for $|x|\gg \lambda$ (such as $v(x)\propto \tanh \big(|x|/\lambda \big)$). We show that the associated particle creation is localized to $|x|\ll \lambda$.

... Optical systems have been developed to simulate Hawking radiation and study entanglement properties [13]. These systems can be described by an effective metric: ...

Dr. Femi Oyewole explores the potential of retrieving information from black holes by leveraging quantum entanglement properties. This paper develops a theoretical framework for information retrieval using quantum entanglement, integrating concepts from Banach space formalism, Hilbert space fragmentation, and the ruliad. By synthesizing recent research on black hole entanglement, Hawking radiation, and wormhole-based quantum teleportation, the study proposes novel methods for quantum information processing across cosmic scales. The findings have profound implications for quantum communication and computing, potentially revolutionizing our understanding of quantum information in extreme gravitational environments.
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

... 1. Acoustic Black Holes: Steinhauer (2016) [53] observed the analogue of Hawking radiation in a BEC, opening up possibilities for studying quantum effects in curved spacetime. ...

This manuscript presents a comprehensive framework for understanding the universe as a vast quantum information network, focusing on the concept of Indefinite Causal Order (ICO) as a potential resolution to the problem of infinities in quantum field theory and quantum gravity. We explore how ICO, which posits that the causal relationship between events at fundamental scales can exist in a quantum superposition, could serve as a natural ultraviolet cutoff, thereby regularizing divergent integrals that plague both quantum field theory and quantum gravity. Our approach leverages recent developments in quantum information theory, holography, and quantum gravity to provide a unified perspective on the nature of reality. We derive key results , including a generalized holographic entropy formula, quantum causal structures, and a complexity-geometry duality. The framework offers new insights into longstanding problems in physics, such as the black hole information paradox and the origin of cosmic structure. We demonstrate that ICO preserves essential principles like gauge invariance and unitarity while fundamentally altering our understanding of causality. Comparative analysis with other approaches to quantum gravity reveals ICO's unique features and potential advantages. We propose experimental tests of our theory, including quantum simulations of holographic models and precision measurements to detect potential Planck-scale effects. This work not only advances our theoretical understanding of the quantum nature of spacetime but also suggests novel approaches to quantum technologies inspired by cosmological principles.

... If a time-independent background becomes supersonic in the flow's direction, sound remains trapped in the supersonic region, and the boundary to the subsonic region becomes an event horizon; thus an analogue black hole (ABH) is formed [18], opening the door to observe Hawking radiation experimentally. On the classical level, this led to the observations of stimulated Hawking emission in water tank setups [19][20][21][22] and the quantum effect of spontaneous Hawking radiation in a Bose-Einstein condensate (BEC) [23][24][25][26][27][28][29]. Other systems enabling Hawking radiation studies are, e.g., fiber optical systems [30,31], superfluid helium [32,33], and photon fluids [34][35][36]. ...

Addressing the general physical question whether spacetime singularities inside black holes exist, we investigate the problem in the context of an analogue system, a flowing laboratory liquid, for which the governing equations are at least in principle known to all relevant scales, and in all regions of the effective spacetime. We suggest to probe the physical phenomena taking place close to a Penrose-type singularity in the interior of a $2+1$D analogue black hole arising from a polytropic, inviscid, irrotational, and axisymmetric steady flow, and propose to this end an experimental setup in a Bose-Einstein condensate. Our study provides concrete evidence, for a well understood dynamical system, that the Einstein equations are not necessary for a singularity to form, demonstrating that Penrose-type spacetime singularities can potentially also exist in non-Einsteinian theories of gravity. Finally, we demonstrate how the singularity is physically avoided in our proposed laboratory setup, and that our analysis can be generalized to three-dimensional flows ($3+1$D analogues).

... We propose using Bose-Einstein condensates (BECs) as an analog system to study the emergence of causal structure in the context of quantum gravity, building on the pioneering work of Steinhauer [66]. This system allows us to explore the connection between emergent causality and spacetime structure, as predicted by our QCE model. ...

This paper introduces the Quantum Causal Emergence (QCE) model, a novel theoretical framework that describes how classical causal structures emerge from quantum processes with indefinite causal order. By integrating concepts from quantum foundations, decoherence theory, and renormalization group methods, we provide a unified description of the quantum-to-classical transition in terms of causal structure. The QCE model employs process matrices and quantum channels to mathematically formulate the transition from indefinite to definite causal order. We propose a mechanism for the emergence of classical causality through decoherence, coarse-graining, and renormalization group flow, offering new perspectives on fundamental problems such as the measurement problem, quantum non-locality, and the emergence of spacetime. We present detailed experimental proposals to test the QCE model using quantum optical systems, superconducting qubits, and analog gravity setups with Bose-Einstein condensates. These experiments aim to probe the transition from indefinite to definite causal order across different physical platforms and scales. The implications of the QCE model extend to quantum computing , where we suggest novel algorithms exploiting indefinite causal order, and to quantum gravity, where we provide insights into the emergence of spacetime and a potential resolution to the black hole information paradox. We also discuss the model's philosophical implications, including a new compatibilist perspective on free will and determinism, and a framework for understanding the nature of time as emergent from causal structures. This work represents a significant advancement in our understanding of quantum causality and its relation to classical physics, potentially revolutionizing our conception of reality at a fundamental level and opening new avenues for quantum technologies and theories of quantum gravity.

... Developing more detailed models of information flow in black hole evaporation based on our gravitational decoherence mechanism.2. Exploring experimental tests of holographic decoherence using analog gravity systems[70].3. Investigating the role of gravitational decoherence in cosmological scenarios, particularly in the context of cosmic inflation and structure formation[41].4. ...

This paper presents a comprehensive exploration of gravitational decoherence as a fundamental mechanism underlying the quantum-to-classical transition. We propose that intrinsic fluctuations in spacetime induce decoherence in quantum systems, providing a universal explanation for the emergence of classical behavior. Our model predicts a decoherence rate that scales with mass and superposition size, becoming significant for macroscopic objects. We derive this rate from first principles and compare it with other decoherence processes, demonstrating its univer-sality. The implications of this model extend to quantum foundations, cosmology, and quantum technologies, potentially resolving long-standing puzzles such as the measurement problem and the origin of cosmic structure. We propose experimental tests, including space-based interferometry, and discuss fundamental limits on quantum technologies. Furthermore, we explore connections with other quantum gravity phenomena, pointing towards a deeper understanding of spacetime as an emergent phenomenon. This work provides a unifying framework for understanding the interface between quantum mechanics and gravity, potentially paving the way for a full theory of quantum gravity.

... Typical analogue spacetimes investigated experimentally are of black holes or cosmic expansion. Arguably, the most celebrated result to date is the observation of the Hawking effect in various systems in the lab [14][15][16][17]. Going beyond the linarised description, there is a growing interest in the backreaction in analogue gravity systems [18][19][20][21][22][23][24][25][26][27][28][29]. ...

Optical solitons classically are stationary solutions of the nonlinear Schr\"odinger equation. We perform a quantum field theoretic treatment by quantising a linearised fluctuation field around the classical soliton solution which can be seen as providing a background spacetime for the field. The linearised fluctuation modifies the soliton background, which is often neglected, reminiscent of the nondepleted-pump approximation. Going beyond this approximation and by using a number-conserving Bogoljubov approach, we find unstable modes that grow as the soliton propagates. Eventually, these unstable modes induce a considerable (backreaction) effect in the soliton. We calculate the backreaction in the classical field fully analytically in the leading second order. The result is a quadratic local decrease of the soliton photon number in propagation due to the backreaction effect of the unstable mode. Provided the initial pulse is close to the classical soliton solution, the unstable mode contributions always become dominant. We also consider practical scenarios for observing this quantum-induced soliton distortion, in the spectral domain. The backreaction, which we expect to be present in bright and dark, discrete and continuous solitons and other nonlinear pulses plays an important role for future optical analogue gravity experiments, for soliton lasers, and optical communications.

... Here, ρ is the density, c s is the speed of sound, and v is the flow velocity. Quantum simulations of Hawking radiation [182] and cosmological particle production [56] provide experimental access to quantum field theory in curved spacetime. We express the Hawking temperature in analog systems as: ...

This manuscript presents a comprehensive framework for understanding the universe as a vast quantum information network. We explore the emergence of spacetime, causality, and locality from fundamental quantum information principles, bridging concepts from quantum mechanics, general relativity, and cosmology. Our approach leverages recent developments in quantum information theory, holography, and quantum gravity to provide a unified perspective on the nature of reality. We derive key results, including a generalized holographic entropy formula, quantum causal structures, and a complexity-geometry duality. The framework offers new insights into longstanding problems in physics, such as the black hole information paradox and the origin of cosmic structure. We propose experimental tests of our theory, including quantum simulations of holographic models and precision measurements to detect potential Planck-scale effects. This work not only advances our theoretical understanding of the quantum nature of spacetime but also suggests novel approaches to quantum technologies inspired by cosmological principles.

... 3. Experiments to probe the quantum nature of black hole horizons: Using analog systems [92]. ...

The reconciliation of quantum mechanics and general relativity remains one of the most profound challenges in modern physics. This paper introduces and rigorously investigates a novel framework proposing that spacetime emerges from quantum entanglement in a lower-dimensional quantum system. We develop a precise mathematical mapping between entanglement structures and geometric properties of emergent spacetime, demonstrating how Einstein's field equations can be derived from fundamental quantum entanglement dynamics. Our approach provides a unified perspective on quantum mechanics and general relativity, offering potential resolutions to long-standing problems, including the black hole information paradox. We extend this framework to cosmological scenarios and discuss experimental predictions, representing a significant step towards a complete theory of quantum gravity. This work not only advances our understanding of the nature of space, time, and gravity as emergent phenomena but also suggests new avenues for empirical investigation of quantum gravitational effects.

... Gravity simulators present an ideal platform where such an enquiry can be pursued. These are physical systems in which excitations behave as though they propagate on a curved spacetime, permitting the experimental * leonardo.solidoro@nottingham.ac.uk investigation of elusive phenomena like Hawking radiation [19][20][21][22] and rotational superradiance [23][24][25][26][27]. Notably, ringdown signals have been studied in polariton superfluids [28], optical solitons [29] and in hydrodynamic systems [30,31]. Although treating these platforms as effectively open systems is usually justified by a combination of energy dissipation, limited temporal evolution and engineering of absorptive boundaries, a complete analysis should not neglect finite-size effects resulting from confinement mechanisms. ...

Astrophysical black holes are open systems which, when perturbed, radiate quasi-normal modes (QNMs) to infinity. By contrast, laboratory analogues are necessarily finite-sized, presenting a potential obstacle to exciting QNMs in the lab. In this study, we investigate how the QNM spectrum of a toy-model black hole is modified when the system is enclosed by a partially reflecting wall. Counter to expectation, we demonstrate that QNMs not only persist in finite-sized systems, but the number of accessible modes increases. Furthermore, we show that QNMs in this set-up can be easily excited by incoherent background noise. Our findings align with studies exploring the spectral stability of black holes, such as those examining small modifications of the surrounding gravitational field. Importantly, our work paves the way for exploring spectral stability in laboratory systems, enabling experimental investigation of black hole features in closed systems.

... This can be performed by setting the integer parameter in Equation (2) to n ̸ = 2. In addition to metamaterials, future research may also be focused on broader connections to analogue gravity models as well as phenomena related to nonlinear optics [28][29][30]. Acknowledgments: The author thanks the Department of Physics and Astronomy (PHAS) at the University of Calgary for their support throughout this research work. ...

The objective of this work is to derive the structure of Minkowski spacetime using a Hermitian spin basis. This Hermitian spin basis is analogous to the Pauli spin basis. The derived Minkowski metric is then employed to obtain the corresponding Lorentz factors, potential Lie algebra, effects on gamma matrices and complex representations of relativistic time dilation and length contraction. The main results, a discussion of the potential applications and future research directions are provided.

In this paper, we employ the Generalized Feshbach-Villars transformation (GFVT) to investigate the relativistic quantum dynamics of spin-0 scalar particles within the backdrop of a magnetic universe characterized by the Bonnor-Melvin cosmological space-time, which exhibits a geometrical topology resulting in an angular deficit. We derive the radial equation of the Klein-Gordon equation using this FV representation and obtain analytical solutions utilizing special functions. Our analysis demonstrates that various parameters associated with the space-time geometry exert significant influence on the eigenvalue solutions within this novel representation.

Reasoning by analogies permeates theoretical developments in physics and astrophysics, motivated by the unreachable nature of many phenomena at play. For example, analogies have been used to understand black hole physics, leading to the development of a thermodynamic theory for these objects and the discovery of the Hawking effect. The latter, which results from quantum field theory on black hole space-times, changed the way physicists approached this subject: what had started as a mere aid to understanding becomes a possible source of evidence via the research programme of “analogue gravity” that builds on analogue models for field effects. Some of these analogue models may and can be realised in the laboratory, allowing experimental tests of field effects. Here, we present a historical perspective on the connection between the Hawking effect and analogue models. We also present a literature review of current research, bringing history and contemporary physics together. We argue that the history of analogue gravity and the Hawking effect is divided into three distinct phases based on how and why analogue models have been used to investigate fields in the vicinity of black holes. Furthermore, we find that modern research signals a transition to a new phase, where the impetus for the use of analogue models has surpassed the problem they were originally designed to solve.

Recent experimental progresses in controlling classical and quantum fluids have made it possible to realize acoustic analogs of gravitational black holes, where a flowing fluid provides an effective spacetime on which sound waves propagate, demonstrating Hawking-like radiation and superradiance. We propose the exciting possibility that new hydrodynamic systems might provide insights to help resolve mysteries associated with quantum gravity, including the black hole information-loss paradox and the removal of spacetime singularities.

One of the exotic expectations in the 2D curved spacetime is the geometric potential from the curvature of the 2D space, still possessing unsolved fundamental questions through Dirac quantization. The atomically thin 2D materials are promising for the realization of the geometric potential, but the geometric potential in 2D materials is not identified experimentally. Here, the curvature‐induced ring‐patterned bound states are observed in structurally deformed 2D semiconductors and formulated the modified geometric potential for the curvature effect, which demonstrates the ring‐shape bound states with angular momentum. The formulated modified geometric potential is analogous to the effective potential of a rotating charged black hole. Density functional theory and tight‐binding calculations are performed, which quantitatively agree well with the results of the modified geometric potential. The modified geometric potential is described by modified Gaussian and mean curvatures, corresponding to the curvature‐induced changes in spin‐orbit interaction and band gap, respectively. Even for complex structural deformation, the geometric potential solves the complexity, which aligns well with experimental results. The understanding of the modified geometric potential provides us with an intuitive clue for quantum transport and a key factor for new quantum applications such as valleytronics, spintronics, and straintronics in 2D semiconductors.

We theoretically investigate the acoustic analogs of high-angular-momentum rotating black holes in exciton-polariton condensates. Performing numerical simulations of a long-lived ring-shaped condensate configuration with an acoustic horizon and ergoregion for high-angular-momentum states, we observed a quasistable state near critical angular momentum where the acoustic black hole horizon disappears. Our findings offer an insight into the quantum nature of the instability of naked singularity.

Signals of entanglement and nonlocality are quantitatively evaluated at zero and finite temperature in an analog black hole realized in the flow of a quasi-one-dimensional Bose-Einstein condensate. The violation of Lorentz invariance inherent to this analog system opens the prospect to observe three-mode quantum correlations and we study the corresponding violation of bipartite and tripartite Bell inequalities. It is shown that the long-wavelength modes of the system are maximally entangled, in the sense that they realize a superposition of continuous variable versions of Greenberger-Horne-Zeilinger states the entanglement of which resists partial tracing.

A Laval nozzle can accelerate expanding gas above supersonic velocities, while cooling the gas in the process. This work investigates this process for microscopic Laval nozzles by means of nonequilibrium molecular dynamics simulations of stationary flow, using grand-canonical Monte Carlo particle reservoirs. We study the steady-state expansion of a simple fluid, a monoatomic gas interacting via a Lennard-Jones potential, through an idealized nozzle with atomically smooth walls. We obtain the thermodynamic state variables pressure, density, and temperature but also the Knudsen number, speed of sound, velocity, and the corresponding Mach number of the expanding gas for nozzles of different sizes. We find that the temperature is well defined in the sense that the each velocity components of the particles obey the Maxwell-Boltzmann distribution, but it is anisotropic, especially for small nozzles. The velocity autocorrelation function reveals a tendency towards condensation of the cooled supersonic gas, although the nozzles are too small for the formation of clusters. Overall we find that microscopic nozzles act qualitatively like macroscopic nozzles in that the particles are accelerated to supersonic speeds while their thermal motion relative to the stationary flow is cooled. We find that, like macroscopic Laval nozzles, microscopic nozzles also exhibit a sonic horizon, which is well defined on a microscopic scale. The sonic horizon is positioned only slightly further downstream compared to isentropic expansion through macroscopic nozzles, where it is situated in the most narrow part. We analyze the sonic horizon by studying space-time density correlations, i.e., how thermal fluctuations at two positions of the gas density are correlated in time and find that after the sonic horizon there are indeed no upstream correlations on a microscopic scale.

Acting as analog models of curved spacetime, surfaces of revolution employed for exploring novel optical effects are followed with great interest nowadays to enhance our comprehension of the universe. It is of general interest to understand the spectral effect of light propagating a long distance in the universe. Here we address the issue of how curved space affects the phenomenon of spectral switches, a spectral sudden change during propagation caused by the finite size of a light source. Based on the point spread function of curved space under the paraxial approximation, the expression of the on-axis output spectrum is derived and calculated numerically. A theoretical way to find on-axis spectral switches is also derived, which interprets the effect of spatial curvature of surfaces on spectral switches as a modification of the effective Fresnel number. We find that the spectral switches on surfaces with positive Gaussian curvature are closer to the source compared with the flat surface case, while the effect is opposite on surfaces with negative Gaussian curvature. We also find that the spectral switches farther away from the light source are more sensitive to the change in Gaussian curvature. This work deepens our understanding of the properties of fully and partially coherent lights propagating on two-dimensional curved space.

Sagnac interference experiment is theoretically analyzed in the curved spacetime of the Rotating Acoustic Black hole metric. The Zero and the infinite Sagnac delay has been analyzed. The geodesic motion in the metric is discussed very briefly to derive the formula for the Sagnac delay. For the first time, the values of the two constant parameters related to the metric of the acoustic black hole have been found to be restricted within certain limit by the use of the formula for the Sagnac delay. The equation for finding the sonic horizon has also been deduced.

Studies of the formation of Landau levels based on the Schrödinger equation for electrons constrained to curved surfaces have a long history. These include as prime examples surfaces with constant negative curvature, like the pseudosphere [A. Comtet, Ann. Phys. 173, 85 (1987)]. Now, topological insulators, hosting Dirac-type surface states, provide a unique platform to experimentally examine such quantum Hall physics in curved space. Hence, extending previous work we consider solutions of the Dirac equation for the pseudosphere for both the case of an overall perpendicular magnetic field and a homogeneous coaxial, thereby locally varying, magnetic field. For both magnetic-field configurations, we provide analytical solutions for spectra and eigenstates. For the experimentally relevant case of a coaxial magnetic field we find that the Landau levels split and one class shows a peculiar scaling ∝B1/4, thereby characteristically differing from the usual linear B and B1/2 dependence of the planar Schrödinger and Dirac case, respectively. We compare our analytical findings to numerical results that we also extend to the case of the Minding surface.

Some aspects of atom-field interactions in curved spacetime are reviewed. Of great interest are quantum radiative and entanglement processes arising out of Rindler and black hole spacetimes, which involve the role of Hawking–Unruh and dynamical Casimir effects. Most of the discussion surrounds the radiative part of interactions. For this, we specifically reassess the conventional understandings of atomic radiative transitions and energy level shifts in curved spacetime. We also briefly outline the status quo of entanglement dynamics study in curved spacetime, and highlight literature related to some novel insights, like entanglement harvesting. On one hand, the study of the role played by spacetime curvature in quantum radiative and informational phenomena has implications for fundamental physics, notably the gravity-quantum interface. In particular, one examines the viability of the Equivalence Principle, which is at the heart of Einstein’s general theory of relativity. On the other hand, it can be instructive for manipulating quantum information and light propagation in arbitrary geometries. Some issues related to nonthermal effects of acceleration are also discussed.

Physics is living an era of unprecedented cross-fertilization among the different areas of science. In this perspective review, we discuss the manifold impact that state-of-the-art cold and ultracold-atomic platforms can have in fundamental and applied science through the development of platforms for quantum simulation, computation, metrology and sensing. We illustrate how the engineering of table-top experiments with atom technologies is engendering applications to understand problems in condensed matter and fundamental physics, cosmology and astrophysics, unveil foundational aspects of quantum mechanics, and advance quantum chemistry and the emerging field of quantum biology. In this journey, we take the perspective of two main approaches, i.e., creating quantum analogues and building quantum simulators, highlighting that independently of the ultimate goal of a universal quantum computer to be met, the remarkable transformative effects of these achievements remain unchanged. We wish to convey three main messages. First, this atom-based quantum technology enterprise is signing a new era in the way quantum technologies are used for fundamental science, even beyond the advancement of knowledge, which is characterised by truly cross-disciplinary research, extended interplay between theoretical and experimental thinking, and intersectoral approach. Second, quantum many-body physics is unavoidably taking center stage in frontier’s science. Third, quantum science and technology progress will have capillary impact on society, meaning this effect is not confined to isolated or highly specialized areas of knowledge, but is expected to reach and have a pervasive influence on a broad range of society aspects: while this happens, the adoption of a responsible research and innovation approach to quantum technologies is mandatory, to accompany citizens in building awareness and future scaffolding. Following on all the above reflections, this perspective review is thus aimed at scientists active or interested in interdisciplinary research, providing the reader with an overview of the current status of these wide fields of research where cold and ultracold-atomic platforms play a vital role in their description and simulation.

A common feature of collapse models and an expected signature of the quantization of gravity at energies well below the Planck scale is the deviation from ordinary quantum-mechanical behavior. Here, we analyze the general consequences of such modifications from the point of view of quantum information theory and we anticipate applications to different quantum systems. We show that quantum systems undergo corrections to the quantum speed limit which, in turn, imply the modification of the Heisenberg limit for parameter estimation. Our results hold for a wide class of scenarios beyond ordinary quantum mechanics. For some nonlocal models inspired by quantum gravity, the bounds are found to oscillate in time, an effect that could be tested in future high-precision quantum experiments.

We consider a sonic black-hole scenario where an atom condensate flows
through a subsonic-supersonic interface. We discuss several criteria that
reveal the existence of nonclassical correlations resulting from the quantum
character of the spontaneous Hawking radiation. We unify previous general work
as applied to Hawking radiation analogs. We investigate the measurability of
the various indicators and conclude that, within a class of detection schemes,
only the violation of quadratic Cauchy-Schwarz inequalities can be discerned.
We show numerical results that further support the viability of measuring deep
quantum correlations in concrete scenarios.

We analyse prospects for the use of Bose-Einstein condensates as condensed-matter systems suitable for generating a generic `effective metric', and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al (2000 Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a long-term view, we ask what the ultimate limits of such a system might be. To this end, we consider a very general version of the nonlinear Schrödinger equation (with a 3-tensor position-dependent mass and arbitrary nonlinearity). Such equations can be used, for example, in discussing Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We demonstrate that at low momenta linearized excitations of the phase of the condensate wavefunction obey a (3 + 1)-dimensional d'Alembertian equation coupling to a (3 + 1)-dimensional Lorentzian-signature `effective metric' that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analogue for the curved spacetime of general relativity. In contrast, at high momenta we demonstrate how one can use the eikonal approximation to extract a well controlled Bogoliubov-like dispersion relation, and (perhaps unexpectedly) recover non-relativistic Newtonian physics at high momenta. Bose-Einstein condensates appear to be an extremely promising analogue system for probing kinematic aspects of general relativity.

We argue that the following three statements cannot all be true: (i) Hawking
radiation is in a pure state, (ii) the information carried by the radiation is
emitted from the region near the horizon, with low energy effective field
theory valid beyond some microscopic distance from the horizon, and (iii) the
infalling observer encounters nothing unusual at the horizon. Perhaps the most
conservative resolution is that the infalling observer burns up at the horizon.
Alternatives would seem to require novel dynamics that nevertheless cause
notable violations of semiclassical physics at macroscopic distances from the
horizon.

Exploiting the fact that light propagation in defocusing nonlinear media can
mimic the transonic flow of an equivalent fluid, we demonstrate experimentally
the formation of an all-optical event horizon in a waveguide structure akin to
a hydrodynamic Laval nozzle. The analogue event horizon, which forms at the
nozzle throat is suggested as a novel platform for analogous gravity
experiments.

A recent experimental claim of the detection of analogue Hawking radiation in
an optical system [PRL 105 (2010) 203901] has led to some controversy [PRL 107
(2011) 149401, 149402]. While this experiment strongly suggests some form of
particle creation from the quantum vacuum (and hence it is per se very
interesting), it is also true that it seems difficult to completely explain all
features of the observations by adopting the perspective of a Hawking-like
mechanism for the radiation. For instance, the observed photons are emitted
parallel to the optical horizon, and the relevant optical horizon is itself
defined in an unusual manner by combining group and phase velocities. This
raises the question: Is this really Hawking radiation, or some other form of
quantum vacuum radiation? Naive estimates of the amount of quantum vacuum
radiation generated due to the rapidly changing refractive index --- sometimes
called the dynamical Casimir effect --- are not encouraging. However we feel
that naive estimates could be misleading depending on the quantitative
magnitude of two specific physical effects: "pulse steepening" and "pulse
cresting". Plausible bounds on the maximum size of these two effects results in
estimates much closer to the experimental observations, and we argue that the
dynamical Casimir effect is now worth additional investigation.

We study several realistic configurations allowing to realize an acoustic
horizon in the flow of a one dimensional Bose-Einstein condensate. In each case
we give an analytical description of the flow pattern, of the spectrum of
Hawking radiation and of the associated quantum fluctuations. Our calculations
confirm that the non local correlations of the density fluctuations previously
studied in a simplified model provide a clear signature of Hawking radiation
also in realistic configurations. In addition we explain by direct computation
how this non local signal relates to short range modifications of the density
correlations.

Acoustic black holes, formed by the boundary between subsonic and supersonic flows, show similarities with gravitational black holes, while being more accessible. We show that Bose-Einstein condensates of exciton polaritons are especially promising. A superfluid polariton flow naturally becomes supersonic because of the finite lifetime. This allows the formation of event horizons in 1D and 2D, exhibiting Hawking emission. The spin structure of polaritons allows designing inter- and intra-universe wormholes. We demonstrate the ``faster-than-sound'' transmission through a pair of wormholes.

Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. To address this issue experimentally, we utilize the analogy between the propagation of fields around black holes and surface waves on moving water. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include surface wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deep-water) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process.

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 non-thermal spectra
with sharp peaks. We find that these peaks are mostly associated to decaying
resonances and only occasionally to dynamical instabilities. Even at achievable
nonzero temperatures, the radiation peaks can be dominated by the spontaneous
emission, i.e. enhanced zero-point fluctuations, and not, as often in analog
models, by stimulated emission.

We have created an analog of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A steplike potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by means of Bragg spectroscopy.

We apply the microscopic Bogoliubov theory of dilute Bose-Einstein condensates to analyze quantum and thermal fluctuations in a flowing atomic condensate in the presence of a sonic horizon. For the simplest case of a step-like horizon, closed-form analytical expressions are found for the spectral distribution of the analog Hawking radiation and for the density correlation function. The peculiar long-distance density correlations that appear as a consequence of the Hawking emission features turns out to be reinforced by a finite initial temperature of the condensate. The analytical results are in good quantitative agreement with first principle numerical calculations. Comment: 11 pages, 7 figures

We study the phonon fluxes emitted when the condensate velocity crosses the speed of sound, i.e., in backgrounds which are analogous to that of a black hole. We focus on elongated one dimensional condensates and on stationary flows. Our theoretical analysis and numerical results are based on the Bogoliubov-de Gennes equation without further approximation. The spectral properties of the fluxes and of the long distance density-density correlations are obtained, both with and without an initial temperature. In realistic conditions, we show that the condensate temperature dominates the fluxes and thus hides the presence of the spontaneous emission (the Hawking effect). We also explain why the temperature amplifies the long distance correlations which are intrinsic to this effect. This confirms that the correlation pattern offers a neat signature of the Hawking effect. Optimal conditions for observing the pattern are discussed, as well as correlation patterns associated with scattering of classical waves. Flows associated with white holes are also considered. Comment: revTeX 4, 55 pages single-column, 19 figures; v2: figure and refs added, typos corrected; v3: twocolumn, refs added/updated, new results, presentation clarified; v4: usefulness of white holes emphasized

It is shown that, in dilute-gas Bose-Einstein condensates, there exist both dynamically stable and unstable configurations which, in the hydrodynamic limit, exhibit a behavior resembling that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states, as in the well-known suggested mechanism for black hole evaporation. We propose a scheme to generate a stable sonic black hole in a ring trap.

Event horizons for fermion quasiparticles naturally arise in moving textures in superconductors and Fermi superfluids. We discuss the example of a planar soliton moving in superfluid 3He-A, which is closely analogous to a charged rotating black hole. The moving soliton will radiate quasiparticles via the Hawking effect at a temperature of about 5 \mu K, and via vacuum polarization induced by the effective `electromagnetic field' and `ergoregion'. Superfluid 3He-A thus appears to be a useful system for experimental and theoretical simulations of quantum effects related to event horizons and ergoregions. Comment: RevTex, 8 pages, 3 figures, submitted to Phys. Rev. D, corrected after referee report

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.

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 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. Comment: Strongly revised version. 5 pages, 3 eps figures

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.

We theoretically study the entanglement of Hawking radiation emitted by an
analogue black hole. We find that this entanglement can be measured by the
experimentally accessible density-density correlation function, which only
requires standard imaging techniques. It is seen that the high energy tail of
the distribution of Hawking radiation should be entangled, whereas the low
energy part is not. This confirms a previous numerical study. The full
Peres-Horodecki criterion is considered, but a significant simplification is
found in the stationary, homogeneous case. Our method applies to systems which
are sufficiently cold that the thermal phonons can be neglected.

We report an experimental study of superfluid hydrodynamic effects in a
one-dimensional polariton fluid flowing along a laterally patterned
semiconductor microcavity and hitting a micron-sized engineered defect. At high
excitation power, superfluid propagation effects are observed in the polariton
dynamics, in particular, a sharp acoustic horizon is formed at the defect
position, separating regions of sub- and super-sonic flow. Our experimental
findings are quantitatively reproduced by theoretical calculations based on a
generalized Gross-Pitaevskii equation. Promising perspectives to observe
Hawking radiation via photon correlation measurements are illustrated.

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 particles reflected
from the inner horizon. We thus observe self-amplifying Hawking radiation.

Experimental searches for the thermal radiation from analogue black holes
require the measurement of very low temperatures in regimes where other thermal
noises may interfere or even mimic the sought-after effect. In this letter, we
parameterize the family of bosonic thermal channels which give rise to such
thermal effects and show that by use of coherent states and homodyne detection
one can rule out the non-Hawking contributions and identify those candidate
sources which arise from Hawking-like processes.

We study the quantum entanglement of the quasiparticle pairs emitted by
analogue black holes. We use a phenomenological description of the spectra in
dispersive media to study the domains in parameter space where the final state
is non-separable. In stationary flows, three modes are involved in each sector
of fixed frequency, and not two as in homogeneous situations. The third
spectator mode acts as an environment for the pairs, and the strength of the
coupling significantly reduces the quantum coherence. The non-separability of
the pairs emitted by white holes are also considered, and compared with that of
black holes.

QUANTUM gravitational effects are usually ignored in calculations of the
formation and evolution of black holes. The justification for this is
that the radius of curvature of space-time outside the event horizon is
very large compared to the Planck length
(Għ/c3)1/2 ~ 10-33 cm, the
length scale on which quantum fluctuations of the metric are expected to
be of order unity. This means that the energy density of particles
created by the gravitational field is small compared to the space-time
curvature. Even though quantum effects may be small locally, they may
still, however, add up to produce a significant effect over the lifetime
of the Universe ~ 1017 s which is very long compared to the
Planck time ~ 10-43 s. The purpose of this letter is to show
that this indeed may be the case: it seems that any black hole will
create and emit particles such as neutrinos or photons at just the rate
that one would expect if the black hole was a body with a temperature of
(κ/2π) (ħ/2k) ~ 10-6 (Msolar/M)K where
κ is the surface gravity of the black hole1. As a black
hole emits this thermal radiation one would expect it to lose mass. This
in turn would increase the surface gravity and so increase the rate of
emission. The black hole would therefore have a finite life of the order
of 1071 (Msolar/M)-3 s. For a black hole of solar
mass this is much longer than the age of the Universe. There might,
however, be much smaller black holes which were formed by fluctuations
in the early Universe2. Any such black hole of mass less than
1015 g would have evaporated by now. Near the end of its life
the rate of emission would be very high and about 1030 erg
would be released in the last 0.1 s. This is a fairly small explosion by
astronomical standards but it is equivalent to about 1 million 1 Mton
hydrogen bombs.

It is shown that the same arguments which lead to black-hole evaporation also predict that a thermal spectrum of sound waves should be given out from the sonic horizon in transsonic fluid flow.

There are a number of similarities between black-hole physics and thermodynamics. Most striking is the similarity in the behaviors of black-hole area and of entropy: Both quantities tend to increase irreversibly. In this paper we make this similarity the basis of a thermodynamic approach to black-hole physics. After a brief review of the elements of the theory of information, we discuss black-hole physics from the point of view of information theory. We show that it is natural to introduce the concept of black-hole entropy as the measure of information about a black-hole interior which is inaccessible to an exterior observer. Considerations of simplicity and consistency, and dimensional arguments indicate that the black-hole entropy is equal to the ratio of the black-hole area to the square of the Planck length times a dimensionless constant of order unity. A different approach making use of the specific properties of Kerr black holes and of concepts from information theory leads to the same conclusion, and suggests a definite value for the constant. The physical content of the concept of black-hole entropy derives from the following generalized version of the second law: When common entropy goes down a black hole, the common entropy in the black-hole exterior plus the black-hole entropy never decreases. The validity of this version of the second law is supported by an argument from information theory as well as by several examples.

We theoretically study the entanglement between phonons spontaneously
generated in atomic Bose-Einstein condensates by analog Hawking and dynamical
Casimir processes. The quantum evolution of the system is numerically modeled
by a truncated Wigner method based on a full microscopic description of the
condensate and state non-separability is assessed by applying a generalized
Peres-Horodecki criterion. The peculiar distribution of entanglement is
described in both real and momentum spaces and its robustness against
increasing initial temperature is investigated. Viable strategies to
experimentally detect the predicted phonon entanglement are briefly discussed.

The Planck distribution of photons emitted by a blackbody led to the development of quantum theory. An analogous distribution of phonons should exist in a Bose-Einstein condensate. We observe this Planck distribution of thermal phonons in a 3D condensate. This observation provides an important confirmation of the basic nature of the condensate's quantized excitations. In contrast to the bunching effect, the density fluctuations are seen to increase with increasing temperature. This is due to the nonconservation of the number of phonons. In the case of rapid cooling, the phonon temperature is out of equilibrium with the surrounding thermal cloud. In this case, a Bose-Einstein condensate is not as cold as previously thought. These measurements are enabled by our in situ k-space technique.

The principle of equivalence, which says that gravity couples to the energy-momentum tensor of matter, and the quantum-mechanical requirement that energy should be positive imply that gravity is always attractive. This leads to singularities in any reasonable theory of gravitation. A singularity is a place where the classical concepts of space and time break down as do all the known laws of physics because they are all formulated on a classical space-time background. In this paper it is claimed that this breakdown is not merely a result of our ignorance of the correct theory but that it represents a fundamental limitation to our ability to predict the future, a limitation that is analogous but additional to the limitation imposed by the normal quantum-mechanical uncertainty principle. The new limitation arises because general relativity allows the causal structure of space-time to be very different from that of Minkowski space. The interaction region can be bounded not only by an initial surface on which data are given and a final surface on which measurements are made but also a "hidden surface" about which the observer has only limited information such as the mass, angular momentum, and charge. Concerning this hidden surface one has a "principle of ignorance": The surface emits with equal probability all configurations of particles compatible with the observers limited knowledge. It is shown that the ignorance principle holds for the quantum-mechanical evaporation of black holes: The black hole creates particles in pairs, with one particle always falling into the hole and the other possibly escaping to infinity. Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state. This means there is no S matrix for the process of black-hole formation and evaporation. Instead one has to introduce a new operator, called the superscattering operator, which maps density matrices describing the initial situation to density matrices describing the final situation.

* Introduction * Experimental and Theoretical Background on He II. * Elementary Excitations * Elementary Excitations in He II * Superfulid Behavior: Response to a Transverse Probe. Qualitative Behavior of a Superfluid * Superfluid Flow: Macroscopic Limit * Basis for the Two-Fluid Model * First, Second, and Quasi-Particle sound * Vortex Lines * Microscopic Theory: Uniform Condensate * Microscopic Theory: Non-Uniform Condensate * Conclusion

We measure the time oscillations of a freely evolving standing wave of phonons in a Bose-Einstein condensate. We present the technique of short Bragg pulses, which stimulates the standing wave. The subsequent oscillations are observed in situ. The frequency of the oscillations gives the dispersion relation, the amplitude gives the static structure factor, and the decay gives the dephasing time. The new technique gives orders of magnitude more sensitivity than Bragg spectroscopy, allowing for the observation of deviations from the local density approximation. Specifically, it is seen that the phonons undergo a transition from three dimensions to one dimension, when their wavelength becomes longer than the transverse radius of the condensate. The one-dimensional regime contains an inflection point in the dispersion relation, a decrease in the superfluid critical velocity, a minimum in the group velocity, and an increase in the lifetime of the standing wave oscillations.

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as
an unequivocal signature of spontaneous Hawking radiation in sonic black holes.
This violation can be particularly large near the peaks in the radiation
spectrum emitted from a resonant boson structure forming a sonic horizon. As a
function of the frequency-dependent Hawking radiation intensity, we analyze the
degree of CS violation and the maximum violation temperature for a double
barrier structure separating two regions of subsonic and supersonic condensate
flow. We also consider the case where the resonant sonic horizon is produced by
a space-dependent contact interaction. In some cases, CS violation can be
observed by direct atom counting in a time-of-flight experiment. We show that
near the conventional zero-frequency radiation peak, the decisive CS violation
cannot occur.

The conflict between the principles of quantum mechanics and those of general relativity reached crisis proportions with the discovery that black holes have a heat content, or entropy. But efforts to solve the problem have since led to profound and revolutionary new insights into the quantum structure of space–time. In this review, I will explain not only the conflict but also the surprising ideas that can resolve the apparent inconsistencies between the two most fundamental theories of physics.

In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects
cause black holes to create and emit particles as if they were hot bodies with temperature
\frachk2pk » 10 - 6 ( \fracM\odot M )° K\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K
where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black
hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon
of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons
in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so
much entropy per baryon.

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.

Event horizons of astrophysical black holes and gravitational analogues have been predicted to excite the quantum vacuum and give rise to the emission of quanta, known as Hawking radiation. We experimentally create such a gravitational analogue using ultrashort laser pulse filaments and our measurements demonstrate a spontaneous emission of photons that confirms theoretical predictions.

We study the stress energy two-point function to show how short distance correlations across the horizon transform into correlations among asymptotic states, for the Unruh effect, and for black hole radiation. In the first case the transition is caused by the coupling to accelerated systems. In the second, the transition is more elusive and due to the change of the geometry from the near horizon region to the asymptotic one. The gradual transition is appropriately described by using affine coordinates. We relate this to the covariant regularization used to evaluate the mean value of the stress energy. We apply these considerations to analogue black holes, i.e. dispersive theories. On one hand, the preferred rest frame gives further insight about the transition, and on the other hand, the dispersion tames the singular behavior found on the horizon in relativistic theories. Comment: 21 pages, 4 figures, new section on growth of correlations

In this article 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.

A moving dielectric medium acts as an effective gravitational field on light. One can use media with extremely low group velocities [Lene Vestergaard Hau et al., Nature (London) 397, 594 (1999)] to create dielectric analogs of astronomical effects on Earth. In particular, a vortex flow imprints a long-ranging topological effect on incident light and can behave like an optical black hole.

Singularities underlie many optical phenomena. The rainbow, for example, involves a particular type of singularity-a ray catastrophe-in which light rays become infinitely intense. In practice, the wave nature of light resolves these infinities, producing interference patterns. At the event horizon of a black hole, time stands still and waves oscillate with infinitely small wavelengths. However, the quantum nature of light results in evasion of the catastrophe and the emission of Hawking radiation. Here I report a theoretical laboratory analogue of an event horizon: a parabolic profile of the group velocity of light brought to a standstill in an atomic medium can cause a wave singularity similar to that associated with black holes. In turn, the quantum vacuum is forced to create photon pairs with a characteristic spectrum, a phenomenon related to Hawking radiation. The idea may initiate a theory of 'quantum' catastrophes, extending classical catastrophe theory.

I present a microscopic description of Hawking radiation in sonic black holes. A one-dimensional Fermi-degenerate liquid squeezed by a smooth barrier forms a transonic flow, a sonic analog of a black hole. The quantum treatment of the noninteracting case establishes a close relationship between sonic Hawking radiation and quantum tunneling through the barrier. Quasiparticle excitations appear at the barrier and are then radiated with a thermal distribution in exact agreement with Hawking's formula. The signature of the radiation can be found in the dynamic structure factor, which can be measured in a scattering experiment. The possibility for experimental verification of this new transport phenomenon for ultracold atoms is discussed.

It is demonstrated that the propagation of electromagnetic waves in an appropriately designed waveguide is (for large wavelengths) analogous to that within a curved space-time--such as around a black hole. As electromagnetic radiation (e.g., microwaves) can be controlled, amplified, and detected (with present-day technology) much easier than sound, for example, we propose a setup for the experimental verification of the Hawking effect. Apart from experimentally testing this striking prediction, this would facilitate the investigation of the trans-Planckian problem.

The physics at the event horizon resembles the behavior of waves in moving media. Horizons are formed where the local speed of the medium exceeds the wave velocity. We used ultrashort pulses in microstructured optical fibers to demonstrate the formation of an artificial event horizon in optics. We observed a classical optical effect: the blue-shifting of light at a white-hole horizon. We also showed by theoretical calculations that such a system is capable of probing the quantum effects of horizons, in particular Hawking radiation.

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 among the quanta emitted at different times, unlike in the usual Hawking effect. These phenomena may be observable in condensed matter black hole analogs that exhibit "superluminal" dispersion. Comment: RevTex, 13 pages, 4 eps figures; minor corrections, final version to be published in Phys. Rev. D

Although slow light (electromagnetically induced transparency) would seem an ideal medium in which to institute a ``dumb hole'' (black hole analog), it suffers from a number of problems. We show that the high phase velocity in the slow light regime ensures that the system cannot be used as an analog displaying Hawking radiation. Even though an appropriately designed slow-light set-up may simulate classical features of black holes -- such as horizon, mode mixing, Bogoliubov coefficients, etc. -- it does not reproduce the related quantum effects. PACS: 04.70.Dy, 04.80.-y, 42.50.Gy, 04.60.-m. Comment: 14 pages RevTeX, 5 figures

- S Finazzi
- I Carusotto

S. Finazzi and I. Carusotto, Phys. Rev. A 90, 033607 (2014).