arXiv subjects

Stefano Finazzi

Publications and source records attributed to Stefano Finazzi.

At least 19 recordsLinked to original sources

arXiv2016

Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems

We present a method to describe driven-dissipative multi-mode systems by considering a truncated hierarchy of equations for the correlation functions. We consider two hierarchy truncation schemes with a global cutoff on the correlation order, which is the sum of the exponents of the operators involved in the correlation functions: a 'hard' cutoff corresponding to an expansion around the vacuum, which applies to a regime where the number of excitations per site is small; a 'soft' cutoff which corresponds to an expansion around coherent states, which can be applied for large excitation numbers per site. This approach is applied to describe the bunching-antibunching transition in the driven-dissipative Bose-Hubbard model for photonic systems. The results have been successfully benchmarked by comparison with calculations based on the corner-space renormalization method in 1D and 2D systems. The regime of validity and strengths of the present truncation methods are critically discussed.

cond-mat.quant-gas↗

arXiv2014

Spontaneous quantum emission from analog white holes in a nonlinear optical medium

We use a microscopic quantum optical model to compute the spectrum of quantum vacuum emission from strong laser pulses propagating in nonlinear optical media. Similarities and differences with respect to the emission of analog white holes as predicted by quantum field theory in curved spacetime are highlighted. Conceptual issues related to the role played by the material dispersion and to the presence or absence of the horizon are clarified. Critical comparison with available experimental data is made.

physics.optics↗

arXiv2013

Entangled phonons in atomic Bose-Einstein condensates

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.

cond-mat.quant-gas↗

arXiv2013

Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse

A strong light pulse propagating in a nonlinear Kerr medium produces a change in the refractive index, which makes light travel at different speeds inside and outside the pulse. By tuning the pulse velocity, an analog black hole horizon can be obtained in a suitable frequency window. In this paper, we develop a quantum theory of light propagation for this system, including the frequency dispersion of the refractive index of the medium by coupling the electromagnetic field to matter polarization fields. In a configuration with a single black hole horizon, the spectrum of spontaneously emitted particles presents some similarities with Hawking radiation. Furthermore, even in horizonless systems spontaneous vacuum emission is still possible due to the dispersive nature of the medium, yet with dramatically different spectral properties.

physics.optics↗

arXiv2012

Analogue gravitational phenomena in Bose-Einstein condensates

Analogue gravity is based on the simple observation that perturbations propagating in several physical systems can be described by a quantum field theory in a curved spacetime. While phenomena like Hawking radiation are hardly detectable in astrophysical black holes, these effects may be experimentally tested in analogue systems. In this Thesis, focusing on Bose-Einstein condensates, we present our recent results about analogue models of gravity from three main perspectives: as laboratory tests of quantum field theory in curved spacetime, for the techniques that they provide to address various issues in general relativity, and as toy models of quantum gravity. The robustness of Hawking-like particle creation is investigated in flows with a single black hole horizon. Furthermore, we find that condensates with two (white and black) horizons develop a dynamical instability known in general relativity as black hole laser effect. Using techniques borrowed from analogue gravity, we also show that warp drives, which are general relativistic spacetimes allowing faster-than-light travel, are unstable. Finally, the cosmological constant issue is investigated from an analogue gravity perspective and relativistic Bose-Einstein condensates are proposed as new analogue systems with novel interesting properties.

gr-qc↗

arXiv2012

Kinematic study of the effect of dispersion in quantum vacuum emission from strong laser pulses

A strong light pulse propagating in a nonlinear medium causes an effective change in the local refractive index. With a suitable tuning of the pulse velocity, the leading and trailing edge of the pulse were predicted to behave as analogue black and white horizons in the limit of a dispersionless medium. In this paper, we study a more realistic situation where the frequency dispersion of the medium is fully taken into account. As soon as positive frequency modes with negative norm are present in the comoving frame, spontaneous emission of quantum vacuum radiation is expected to arise independently of the presence of horizons. We finally investigate the kinematic constraints put on the emission and we show that the optimal directions to observe Hawking-like emission form a narrow angle with the direction of propagation of the pulse.

physics.optics↗

arXiv2012

The analogue cosmological constant in Bose-Einstein condensates: a lesson for quantum gravity

For almost a century, the cosmological constant has been a mysterious object, in relation to both its origin and its very small value. By using a Bose-Einstein condensate analogue model for gravitational dynamics, we address here the cosmological constant issue from an analogue gravity standpoint. Starting from the fundamental equations describing a system of condensed bosons, we highlight the presence of a vacuum source term for the analogue gravitational field, playing the role of a cosmological constant. In this simple system it is possible to compute from scratch the value of this constant, to compare it with other characteristic energy scales and hence address the problem of its magnitude within this framework, suggesting a different path for the solution of this longstanding puzzle. We find that, even though this constant term is related with quantum vacuum effects, it is not immediately related to the ground state energy of the condensate. On the gravity side this result suggests that the interpretation and computation of the cosmological term as a form of renormalized vacuum energy might be misleading, its origin being related to the mechanism that instead produces spacetime from its pregeometric progenitor, shedding a different light on the subject and at the same time suggesting a potentially relevant role of analogue models in the understanding of quantum gravity.

gr-qc↗

arXiv2012

Hawking radiation in dispersive theories, the two regimes

We compute the black hole radiation spectrum in the presence of high-frequency dispersion in a large set of situations. In all cases, the spectrum diverges like the inverse of the Killing frequency. When studying the low-frequency spectrum, we find only two regimes: an adiabatic one where the corrections with respect to the standard temperature are small, and an abrupt one regulated by dispersion, in which the near-horizon metric can be replaced by step functions. The transition from one regime to the other is governed by a single parameter which also governs the net redshift undergone by dispersive modes. These results can be used to characterize the quasiparticles spectrum of recent and future experiments aiming to detect the analogue Hawking radiation. They also apply to theories of quantum gravity which violate Lorentz invariance.

gr-qc↗

arXiv2012

Impossibility of superluminal travel in Lorentz violating theories

Warp drives are space-times allowing for superluminal travel. However, they are quantum mechanically unstable because they produce a Hawking-like radiation which is blue shifted at their front wall without any bound. We reexamine this instability when local Lorentz invariance is violated at ultrahigh energy by dispersion, as in some theories of quantum gravity. Interestingly, even though the ultraviolet divergence is now regulated, warp drives are still unstable. Moreover the type of instability is different whether one uses a subluminal or a superluminal dispersion relation. In the first case, a black-hole laser yields an exponential amplification of the emitted flux whereas, in the second, infrared effects produce a linear growth of that flux. These results suggest that chronology could still be protected when violating Lorentz invariance.

gr-qc↗

arXiv2012

Cosmological Constant: A Lesson from Bose-Einstein Condensates

The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of the cosmological constant would require a detailed understanding about how Einstein equations emerge from the full microscopic quantum theory. In this light, the cosmological constant appears as a decisive test bench for any quantum or emergent gravity scenario.

gr-qc↗

arXiv2012

Black hole radiation with short distance dispersion, an analytical S-matrix approach

Local and non-local properties of Hawking radiation in the presence of short distance dispersion are computed using connection formulae. The robustness of the spectrum and that of the two-point function are explained by showing that the leading deviations from the relativistic expressions decrease with the inverse of the spatial extension of the near horizon region. This region corresponds to a portion of de Sitter space with a preferred frame. We show that the phases of the Bogoliubov coefficients are relevant for the two-point function in black and white holes, and also for the black hole laser effect. We also present an unexpected relation between the spectra obtained with sub and with superluminal dispersion and we apply our formalism to massive fields. Our predictions are validated by numerical analysis.

hep-th↗

arXiv2011

Spectral properties of acoustic black hole radiation: Broadening the horizon

The sensitivity of the black hole spectrum when introducing short distance dispersion is studied in the context of atomic Bose condensates. By considering flows characterized by several length scales, we show that, while the spectrum remains remarkably Planckian, the temperature is no longer fixed by the surface gravity. Rather it is determined by the average of the flow gradient across the horizon over an interval fixed by the healing length and the surface gravity, as if the horizon were broadened. This remains valid as long as the flow does not induce nonadiabatic effects that produce oscillations or some parametric amplification of the flux.

gr-qc↗

arXiv2011

On the robustness of acoustic black hole spectra

We study the robustness of the spectrum emitted by an acoustic black hole by considering series of stationary flows that become either subsonic or supersonic, i.e. when the horizon disappears. We work with the superluminal Bogoliubov dispersion of Bose--Einstein condensates. We find that the spectrum remains remarkably Planckian until the horizon disappears. When the flow is everywhere supersonic, new pair creation channels open. This will be the subject of a forthcoming work.

gr-qc↗

arXiv2010

Black hole lasers in Bose-Einstein condensates

We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density-density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as a self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.

cond-mat.quant-gas↗

arXiv2010

Relativistic Bose-Einstein Condensates: a new system for analogue models of gravity

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

gr-qc↗

arXiv2010

On the impossibility of superluminal travel: the warp drive lesson

The question of whether it is possible or not to surpass the speed of light is already centennial. The special theory of relativity took the existence of a speed limit as a principle, the light postulate, which has proven to be enormously predictive. Here we discuss some of its twists and turns when general relativity and quantum mechanics come into play. In particular, we discuss one of the most interesting proposals for faster than light travel: warp drives. Even if one succeeded in creating such spacetime structures, it would be still necessary to check whether they would survive to the switching on of quantum matter effects. Here, we show that the quantum back-reaction to warp-drive geometries, created out of an initially flat spacetime, inevitably lead to their destabilization whenever superluminal speeds are attained. We close this investigation speculating the possible significance of this further success of the speed of light postulate.

gr-qc↗

arXiv2009

Semiclassical instability of dynamical warp drives

Warp drives are very interesting configurations in General Relativity: At least theoretically, they provide a way to travel at superluminal speeds, albeit at the cost of requiring exotic matter to exist as solutions of Einstein's equations. However, even if one succeeded in providing the necessary exotic matter to build them, it would still be necessary to check whether they would survive to the switching on of quantum effects. Semiclassical corrections to warp-drive geometries have been analyzed only for eternal warp-drive bubbles traveling at fixed superluminal speeds. Here, we investigate the more realistic case in which a superluminal warp drive is created out of an initially flat spacetime. First of all we analyze the causal structure of eternal and dynamical warp-drive spacetimes. Then we pass to the analysis of the renormalized stress-energy tensor (RSET) of a quantum field in these geometries. While the behavior of the RSET in these geometries has close similarities to that in the geometries associated with gravitational collapse, it shows dramatic differences too. On one side, an observer located at the center of a superluminal warp-drive bubble would generically experience a thermal flux of Hawking particles. On the other side, such Hawking flux will be generically extremely high if the exotic matter supporting the warp drive has its origin in a quantum field satisfying some form of Quantum Inequalities. Most of all, we find that the RSET will exponentially grow in time close to, and on, the front wall of the superluminal bubble. Consequently, one is led to conclude that the warp-drive geometries are unstable against semiclassical back-reaction.

gr-qc↗

arXiv2008

On the stability of shocks with particle pressure

We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy/vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion. We show that, due to particle diffusion into the upstream region, the fluid will be perturbed also upstream: we treat these perturbation in the short wavelength (WKBJ) regime. We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself: this global mode requires the new modes. Then, using the perturbed Rankine-Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency. We solve numerically the equations for the eigenfrequency in the WKBJ regime for the models of Amato and Blasi (2005), showing that they are stable. We then discuss the differences between our treatment and previous work.

astro-ph↗