The scattering of sound wave perturbations from vortex excitations of Bose-Einstein condensates (BEC) is investigated by numerical integration of the associated Klein-Gordon equation. It is found that, at sufficiently high angular speeds, sound wave-packets can extract a sizeable fraction of the vortex energy through a mechanism of superradiant scattering. It is conjectured that this superradiant regime may be detectable in BEC experiments.PACS numbers: 03.75.Lm Recent years have witnessed a growing interest in pursuing analogue models of gravitational physics in condensed matter systems. The rationale for such models traces back to a seminal observation by Unruh [1], who noted a close analogy between sound wave propagation in an inhomogeneous background flow and field propagation in curved space-time. The analogy goes on by observing that, much like superfluid hydrodynamics is a large-scale effective theory of microscopic superfluids, field theory on a curved space-time might also be regarded as a large-scale limit of a possible microscopic formulation of quantum gravity. The crucial point is that, whereas microscopic theories of quantum gravity are still largely a matter of speculation, the microscopic theory of superfluids is well developed. It can thus be hoped that the wide body of knowledge available for the latter can be brought to the benefit of the former [2]. For instance, assessing the mechanisms of sound radiation from 'terrestrial black holes' beyond the hydrodynamic picture may in principle offer new insights into the microscopic origin of cosmic black hole radiance, the Hawking effect, and other cosmological phenomena.A key step along this long-term program is the study of scattering and radiance phenomena from black holes whose background space-time can be associated with fluid excitations such as vortices. A model of fluid flow which seems particularly well suited to pursue the 'analogue gravity' program is the so-called draining-bathtub geometry [3], namely a three-dimensional flow with a sink (vortex) at the origin. The flow field induced by the vortex is associated with an acoustic metric with two crucial ingredients of black hole physics: an event horizon and an ergosphere. The former is a spatial surface which allows only one-way propagation of physical signals (from the outside into the vortex), while the latter is a region from which part of the the vortex energy can be extracted via the mechanism of superradiance.Such a phenomenon was first studied by Zel'dovich [4] with regard to the generation of waves by a rotating body * Electronic address: fr.federici@sns.it and was then analysed as stimulated emission in blackhole radiance [5,6,7]. Superresonance is an acousticwave version of the Penrose [8] process, whereby a planewave solution of a scalar massless field in the black hole background is scattered from the ergosphere with an amplification at the expenses of the rotational energy of the black hole. Such process has been shown to occur in a certain class of analogue (2+1)-dimension...

We use hydrodynamic equations to study sound propagation in a superfluid Fermi gas inside a strongly elongated cigar-shaped trap, with main attention to the transition from the BCS to the unitary regime. We treat first the role of the radial density profile in the quasi-onedimensional limit and then evaluate numerically the effect of the axial confinement in a configuration in which a hole is present in the gas density at the center of the trap. We find that in a strongly elongated trap the speed of sound in both the BCS and the unitary regime differs by a factor 3/5 from that in a homogeneous three-dimensional superfluid. The predictions of the theory could be tested by measurements of sound-wave propagation in a set-up such as that exploited by M.R. Andrews et al. [Phys. Rev. Lett. 79, 553 (1997)] for an atomic Bose-Einstein condensate.Strong evidence for a superfluid state in ultracold Fermi gases near a Feshbach resonance has come from experimental studies using as probes ballistic expansion [1,2,3,4,5], collective modes [6,7], RF spectroscopy [8], and the generation of quantized vortices [9]. Since the BCS weak-coupling limit and the unitary strongcoupling limit are characterized by the same collectivemode frequencies and expansion dynamics [10], attention has been drawn to the study of sound-wave propagation as allowing a clear identification of these two regimes. In particular Ho [11] and Heiselberg [12] have evaluated the speed of first and second sound in a homogeneous Fermi superfluid as functions of the coupling regime. At low temperature the first sound velocity is given by u 1 = v F (1 + (2/π)hk F a)/3 ≃ v F / √ 3 in the dilute BCS limit and by u 1 ≃ 0.37v F in the unitary limit.Here v F and k F are the Fermi velocity and wavenumber, while a is the s-wave scattering length.The main purpose of this Letter is to evaluate the propagation of density perturbations in a superfluid Fermi gas as a function of coupling strength in an experimentally realizable set-up. This simulates the set-up used in the experiments of Andrews et al.[13] on the propagation of sound pulses along the axis of an elongated cloud of Bose-Einstein condensed 23 Na atoms. In their experiments a density perturbation is generated by turning on a laser at the center of the trap and two pulses propagate in opposite directions along the trap axis. We describe the dynamics of density fluctuations in the superfluid by hydrodynamic equations, namely the continuity equation ∂ t n + ∇ · (nv) = 0(1) and the Euler equationfor the time-dependent density profile n(r, t) and velocity field v(r, t) of the trapped gas. The equation of state enters through the density-dependent chemical potential µ(n), and V (r) describes the external potentials.The laser beam is simulated in our study by a timeindependent effective potential U (z) = U 0 e −z 2 /w 2 having amplitude U 0 and width w, which is turned on at the center of the trap. The Q1D configuration. We discuss first the quasionedimensional (Q1D) case corresponding to V (r) = mω 2 ⊥ r 2 ⊥ /2, where ω...

We present paraconductivity (AL) measurements in three different high temperature superconductors: a melt textured Y Ba2Cu3O7 sample, a Bi2Sr2CaCu2O8 epitaxial thin film and a highly textured Bi2Sr2Ca2Cu3O10 tape. The crossovers between different temperature regimes in excess conductivity have been analysed. The Lawrence-Doniach (LD) crossover, which separates the 2D and 3D regimes, shifts from lower to higher temperatures as the compound anisotropy decreases. Once the LD crossover is overcome, the fluctuation conductivity of the three compounds shows the same universal behaviour: for ǫ = ln T /Tc > 0.23 all the curves bend down according to the 1/ǫ 3 law. This asymptotic behaviour was theoretically predicted previously for the high temperature region where the short wavelength fluctuations (SWF) become important.

The scattering process of a dynamic perturbation impinging on a draining-tub model of an acoustic black hole is numerically solved in the time domain. Analogies with real black holes of General Relativity are explored by using recently developed mathematical tools involving finite elements methods, excision techniques, and constrained evolution schemes for strongly hyperbolic systems. In particular it is shown that superradiant scattering of a quasi-monochromatic wavepacket can produce strong amplification of the signal, offering the possibility of a significant extraction of rotational energy at suitable values of the angular frequency of the vortex and of the central frequency of the wavepacket. The results show that theoretical tools recently developed for gravitational waves can be brought to fruition in the study of other problems in which strong anisotropies are present.