Recent publications by QG-LAB

Selected publications

On the observation of nonclassical excitations in Bose-Einstein condensates

25 Jan 2016

In the recent experimental and theoretical literature well-established nonclassicality criteria from the field of quantum optics have been directly applied to the case of excitations in matter-waves. Among these are violations of Cauchy–Schwarz inequalities, Glauber–Sudarshan P-nonclassicality, sub-Poissonian number-difference squeezing (also known as the two-mode variance) and the criterion of nonseparability. We review the strong connection of these criteria and their meaning in quantum optics, and point out differences in the interpretation between light and matter waves. We then calculate observables for a homogeneous Bose–Einstein condensate undergoing an arbitrary modulation in the interaction parameter at finite initial temperature, within both the quantum theory as well as a classical reference. We conclude that to date in experiments relevant for this scenario nonclassical effects have not conclusively been observed and conjecture that additional, noncommuting, observables have to be measured to this end. Moreover this has important implications for proposed analog gravity models where the observation of nonclassical effects is a major goal.

An acoustic probe for quantum vorticity in Bose-Einstein condensates

2 Apr 2015

Abstract: We investigate the deformation of wavefronts of sound waves in rotating Bose-Einstein condensates. In irrational fluid flows Berry et al. identified this kind of deformation as the hydrodynamic analogue of the Aharonov-Bohm effect. We study this effect in Bose-Einstein condensates and obtain the Aharonov-Bohm phase shift at all wavelengths. We show that this deformation of wave fronts is seen in both phase and density fluctuations. For wavelengths larger than the healing length, the phase fluctuations experience a phase shift of the order of 2π times the winding number. We also consider lattices of vortices. If the angular momentum of the vortices are aligned, the total phase shift is 2π times the number of vortices in the condensate. Because of this behaviour the hydrodynamic Aharonov-Bohm effect can be utilized as a probe for quantum vorticity, whose experimental realization could offers an alternative route to investigate quantum turbulence in the laboratory.

Rotating black holes in a draining bathtub: superradiant scattering of gravity waves

6 Nov 2014

Abstract: In a draining rotating fluid flow background, surface perturbations behave as a scalar field on a rotating effective black hole spacetime. We propose a new model for the background flow which takes into account the varying depth of the water. Numerical integration of the associated Klein-Gordon equation using accessible experimental parameters shows that gravity waves in an appropriate fre- quency range are amplified through the mechanism of superradiance. Our numerical results suggest that the observation of this phenomenon in a common fluid mechanical system is within experi- mental reach. Unlike the case of wave scattering around Kerr black holes, which depends only on one dimensionless background parameter (the ratio a/M between the specific angular momentum and the mass of the black hole), our system depends on two dimensionless background parameters, namely the normalized angular velocity and surface gravity at the effective black hole horizon. 

Reducing Spacetime to Binary Information

September 5, 2012

Abstract: We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is ergodic in the class of space-time manifolds respecting coordinate invariance of general relativity. Space-time fluctuations can be represented in a classical lattice gas model whose Boltzmann weights are constructed with the discretized form of the Einstein-Hilbert action. Within this framework, it is possible to compute basic quantities such as the Ricci curvature tensor and the Einstein equations, and to evaluate the path integral of discrete gravity. The description as a lattice gas model also provides a novel way of quantization and, at the same time, to quantum simulation of fluctuating space-time.

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Analogue gravity literature

Carlos Barceló and Stefano Liberati and Matt Visser

Analogue Gravity

Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

W. G. Unruh

Experimental Black-Hole Evaporation?

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.

Steven Corley and Ted Jacobson

Hawking spectrum and high frequency dispersion

We study the spectrum of created particles in two-dimensional black hole geometries for a linear, Hermitian scalar field satisfying a Lorentz noninvariant field equation with higher spatial derivative terms that are suppressed by powers of a fundamental momentum scale k0. The preferred frame is the "free-fall frame" of the black hole. This model is a variation of Unruh's sonic black hole analogy. We find that there are two qualitatively different types of particle production in this model: a thermal Hawking flux generated by "mode conversion" at the black hole horizon, and a nonthermal spectrum generated via scattering off the background into negative free-fall frequency modes. This second process has nothing to do with black holes and does not occur for the ordinary wave equation because such modes do not propagate outside the horizon with positive Killing frequency. The horizon component of the radiation is astonishingly close to a perfect thermal spectrum: for the smoothest metric studied, with Hawking temperature TH≃0.0008k0, agreement is of order (THk0)3 at frequency ω=TH, and agreement to order THk0 persists out to ωTH≃45 where the thermal number flux is ∼10−20. The flux from scattering dominates at large ω and becomes many orders of magnitude larger than the horizon component for metrics with a "kink," i.e., a region of high curvature localized on a static world line outside the horizon. This nonthermal flux amounts to roughly 10% of the total luminosity for the kinkier metrics considered. The flux exhibits oscillations as a function of frequency which can be explained by interference between the various contributions to the flux.

W. G. Unruh

Sonic analogue of black holes and the effects of high frequencies on black hole evaporation

The naive calculation of black hole evaporation makes the thermal emission depend on the arbitrary high frequency behavior of the theory where the theory is certainly wrong. Using the sonic analogue to black holes, ‘‘dumb holes,’’ I show numerically that a change in the dispersion relation at high frequencies does not seem to alter the evaporation process, lending weight to the reality of the black hole evaporation process. I also suggest a reason for the insensitivity of the process to the high frequency regime.

Ralf Schützhold and William G. Unruh

Gravity wave analogues of black holes

It is demonstrated that gravity waves of a flowing fluid in a shallow basin can be used to simulate phenomena around black holes in the laboratory. Since the speed of the gravity waves as well as their high-wave-number dispersion (subluminal vs superluminal) can be adjusted easily by varying the height of the fluid (and its surface tension) this scenario has certain advantages over the sonic and dielectric black hole analogs, for example, although its use in testing quantum effects is dubious. It can be used to investigate the various classical instabilities associated with black (and white) holes experimentally, including positive and negative norm mode mixing at horizons.

Silke Weinfurtner, Edmund W. Tedford, Matthew C. J. Penrice, William G. Unruh, and Gregory A. Lawrence

Measurement of Stimulated Hawking Emission in an Analogue System

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.

Piyush Jain, Silke Weinfurtner, Matt Visser, and C. W. Gardiner

Analog model of a Friedmann-Robertson-Walker universe in Bose-Einstein condensates: Application of the classical field method

Analog models of gravity have been motivated by the possibility of investigating phenomena not readily accessible in their cosmological counterparts. In this paper, we investigate the analog of cosmological particle creation in a Friedmann-Robertson-Walker universe by numerically simulating a Bose-Einstein condensate with a time-dependent scattering length. In particular, we focus on a two-dimensional homogeneous condensate using the classical field method via the truncated Wigner approximation. We show that for various forms of the scaling function the particle production is consistent with the underlying theory in the long wavelength limit. In this context, we further discuss the implications of modified dispersion relations that arise from the microscopic theory of a weakly interacting Bose gas.

J.-C. Jaskula, G. B. Partridge, M. Bonneau, R. Lopes, J. Ruaudel, D. Boiron, and C. I. Westbrook

Acoustic Analog to the Dynamical Casimir Effect in a Bose-Einstein Condensate

We have modulated the density of a trapped Bose-Einstein condensate by changing the trap stiffness, thereby modulating the speed of sound. We observe the creation of correlated excitations with equal and opposite momenta, and show that for a well-defined modulation frequency, the frequency of the excitations is half that of the trap modulation frequency.

Steven Corley and Ted Jacobson

Black hole lasers

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 analogues that exhibit “superluminal” dispersion.

Antonin Coutant and Renaud Parentani

Black hole lasers, a mode analysis

We show that the black hole laser effect discovered by Corley and Jacobson should be described in terms of frequency eigenmodes that are spatially bound. The spectrum contains a discrete and finite set of complex frequency modes, which appear in pairs and which encode the laser effect. In addition, it contains real frequency modes that form a continuous set when space is infinite, and which are only elastically scattered, i.e., not subject to any Bogoliubov transformation. The quantization is straightforward, but the calculation of the asymptotic fluxes is rather involved. When the number of complex frequency modes is small, our expressions differ from those given earlier. In particular, when the region between the horizons shrinks, there is a minimal distance under which no complex frequency mode exists, and no radiation is emitted. Finally, we relate this effect to other dynamical instabilities found for rotating black holes and in electric fields, and we give the conditions to get this type of instability.

Jeff Steinhauer

Observation of self-amplifying Hawking radiation in an analogue black-hole laser

By a combination of quantum field theory and general relativity, black holes have been predicted to emit Hawking radiation. Observation from an actual black hole is, however, probably extremely difficult, so attention has turned to analogue systems in the search for such radiation. Here, we create a narrow, low density, very low temperature atomic Bose–Einstein condensate, containing an analogue black-hole horizon and an inner horizon, as in a charged black hole. We report the observation of Hawking radiation emitted by this black-hole analogue, which is the output of the black-hole laser formed between the horizons. We also observe the exponential growth of a standing wave between the horizons, which 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.
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If you got interested in analogue gravity you might find the following papers interesting. We will extend this list, but even then this collection is by no means complete. (The focuss is also on particular media, and for exmaple all the analogue gravity studies in optical systems are not listed below. More information on references on optical systems can be found in the first reference listed below, or for example on Daniel Faccio's website.)