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arXiv:gr-qc/0503089 · Physical Review A

Superradiance from hydrodynamic vortices: A numerical study

F. Federici, Christian Cherubini, Sauro Succi A, M. P. Tosi

Published Mar 8, 2006• 53 citations
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Abstract

The scattering of sound-wave perturbations from vortex excitations in hydrodynamic systems with typical Bose-Einstein-condensate (BEC) parameters is investigated by numerical integration of the associated Klein-Gordon equation. The simulations indicate that at sufficiently high angular speeds, in the perturbative limit where back-reaction effects can be neglected, sound wave packets can extract a sizable fraction of the vortex energy through a mechanism of superradiant scattering. It is conjectured that this superradiant regime may be detectable in BEC experiments.

DOI
10.1103/physreva.73.033604

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The scattering of sound-wave perturbations from vortex excitations in hydrodynamic systems with typical Bose-Einstein-condensate (BEC) parameters is investigated by numerical integration of the associated Klein-Gordon equation. The simulations indicate that at sufficiently high angular speeds, in the perturbative limit where back-reaction effects can be neglected, sound wave packets can extract a sizable fraction of the vortex energy through a mechanism of superradiant scattering. It is conjectured that this superradiant regime may be detectable in BEC experiments.
The analogy between the propagation of a massless scalar field in curved spacetime and the propagation of sound waves in a Bose-Einstein Condensate (BEC) gives rise to the possibility of observing the analogues of black hole radiance effects, such as Hawking Radiation and superradiance, in the laboratory. In order to provide a solid foundation for realising such analogue gravity models in an experimental setting, we have conducted a numerical investigation of phonon scattering from a BEC vortex by solving the time-dependent Gross-Pitaevskii (GP) equation, describing the dynamics of dilute gas BECs. The consideration of phonon superradiance in BECs in advance of Hawking Radiation is motivated by the fact superradiance may be easier to detect. ¶ We first present the results of one-dimensional simulations of sound waves propagating in a BEC and reflecting from a vortex-like density profile. Using these results as a guide, two-dimensional simulations of sound propagation in a BEC, and reflection from a BEC vortex, are performed. The technique of propagating the wavefunction in imaginary time was employed to find the vortex ground state. The accuracy of the simulations and the convergence of the solution to the vortex ground state was verified using a range of numerical diagnostics. Finally, preliminary simulations were performed within the superradiant frequency regime for the purposes of determining whether the amplification of incoming waves occurs given an appropriate choice of parameters. Overall, the two-dimensional modelling of reflection of cylindrical waves from a BEC vortex provides a basis for a systematic study of phonon superradiance in BECs.
Abstract The propagation of acoustic perturbations in the velocity potential of a Bose–Einstein condensate (BEC) behave like minimally coupled massless scalar fields in a curved (1 + 1) dimensional Lorentzian space-time, where their propagation is governed by the Klein–Gordon wave equation. For linearized perturbations, this geometric picture can still apply in the presence of a single vortex state of the BEC. Thus far, the amplified scattering of axisymmetric perturbations from a vortex, as a manifestation of the acoustic superradiance, has been investigated by assuming a constant background density of the condensate. This paper addresses the validity of this approximation within the same theoretical workframe, by employing a self-consistent density profile that is obtained by solving the Gross–Pitaevskii equation for an unbound BEC and an approximation to the numerical solution is used throughout the paper. The resulting radial density profile around the vortex implies a radially varying speed of sound, which modifies the entire propagation dynamics as well as the loci of the event horizon and the ergosphere. We investigate the superradiance in temporal domain and, through an independent asymptotic formulation, in the spectral domain. The main conclusions are that the self-consistent density profile remedies the overshoot of the superradiance dynamics temporally and that the spectral profile of the superradiance differs significantly in the vortex-scaled low frequency regime between the constant density and self-consistent density formulations.
We consider the scattering of an acoustic wave from a vortex induced by optical superradiance. The vortex is created by pumping a large amount of angular momentum with a Laguerre-Gaussian light beam in an atomic Bose-Einstein condensate. We derive the mean-field dynamical equations of the light-superfluid system, and obtain the equations governing the elementary excitation of the system, which result in a massless Klein-Gordon equation with source terms. This equation describes the propagation of the sound wave in an effective space-time. Employing a simplifying draining bathtub model for the vortex, we investigate the scattering of the acoustic wave in the vortex phase and obtain a condition for the acoustic superradiance. We conclude that Laguerre-Gaussian-beam-induced sudden transition from homogeneous to vortex state in the superfluid leads to a prominent observation of the acoustic superradiance.
The creation of a topological vortex by a superradiant scattering of a Laguerre-Gaussian (LG) beam off an atomic Bose-Einstein condensate (BEC) is theoretically investigated. It is shown that scattered superradiant radiation can be either in a Gaussian mode without angular momentum or in a LG mode with angular momentum. The conditions leading to these two qualitatively distinct regimes of superradiance are determined in terms of the width for the pump laser and the condensate size for the limiting cases where the recoil energy is both much smaller and larger than the atomic interaction energy.
Abstract Rotational superradiance affects the dynamics of many rotating systems in nature, through either stimulated or spontaneous extraction of energy and angular momentum. By now, this process is well-studied in the relativistic setting, where systems are intrinsically dispersion-free. In many condensed matter systems, however, dispersion is an unavoidable aspect of the description for the short wavelength modes. For these systems, how might one expect superradiance to be modified? In this work, an answer to this question is provided using an illustrative example. The scattering of linear excitations of a Bose–Einstein condensate (BEC) are studied in the presence of a rotating, draining vortex flow using the full Bogoliubov dispersion relation. It is shown that dispersion suppresses the extraction of energy and angular momentum, firstly, by decreasing the superradiant bandwidth, and secondly, by preventing high-angular momentum modes from superradiating.
This paper investigates the acoustic superradiance of the density and phase fluctuations from the single vortex state of a Bose-Einstein condensate, by employing full time-domain and asymptotic frequency domain numerical calculations. The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the axisymmetric density and phase fluctuations in the condensate are governed by the massless scalar Klein-Gordon wave equation, which establishes the rotating black-hole analogy. Hence, the amplified scattering of these fluctuations from the vortex comprise the superradiance effect. A particular coordinate transformation is applied to reveal the event horizon and the ergosphere termwise in the metric and the respective asymptotic spectral solutions. A comparative analysis of the time domain and asymptotic frequency domain results are given for a range of rotational speed of the vortex and the frequency of the impinging fluctuations. The agreement at low rotational speeds of the vortex is shown to be very good, which starts to deteriorate at higher rotational speeds due to increasing constraint violations of the time-domain calculations. We further demonstrate an asymptotic upper bound for the superradiance as a function of vortex rotational speed, provided that the vortex remains stable.