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arXiv:1401.1077 · Physical Review A

Acoustic superradiance from an optical-superradiance-induced vortex in a Bose-Einstein condensate

Nader Ghazanfari, Özgür Esat Müstecaplıoğlu

Published Apr 24, 2014• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.89.043619

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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 A vortex formed in the superfluid state of a Bose-Einstein condensate may exhibit superradiance a la blackhole for radially propagating acoustic fluctuations. The analogy is usually based on the so-called draining bathtub model of the vortex, in which an event horizon and ergosphere emerges when the radial velocity of the superfluid exceeds the propagation speed of sound in the condensate. The acoustic fluctuations mimic a massless scalar field in the curved Lorentzian space-time of the vortex and are governed by the Klein-Gordon wave equation. One common main approximation is the constant background density of the superfluid even in the presence of the vortex. This sets a constant relativistic sound speed. However, the vortex state solution of the Gross-Pitaevskii equation clearly shows that both the density and the speed of sound vary radially near the vortex core, where the event horizon and thus the superradiance will take place. What changes would this complex interdependence bring to the formulation and to the outcomes of the superradiance based on constant density approximation? Here, we recount this question posed under the guidance of Prof. Tekin Dereli and present recent results. We show that the self-consistent density modifies the amplification dynamics near the event horizon significantly, thereby altering the temporal and spectral fingerprint of the superradiance of the vortex.
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.
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.
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 exchange of orbital angular momentum (OAM) between paraxial optical vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In this paper, we develop a theory for the microscopic interaction between matter and an optical vortex beyond paraxial approximation. We show how superposition of vortex states of BEC can be created with a focused optical vortex. Since the polarization or spin angular momentum (SAM) of the optical field is coupled with OAM of the field, in this case, these angular momenta can be transferred to the internal electronic and external center-of-mass motion of atoms provided both the motions are coupled. We propose a scheme for producing the superposition of matter-wave vortices using Gaussian and a focused Laguerre-Gaussian beam. We study how two-photon Rabi frequencies of stimulated Raman transitions vary with focusing angles for different combinations of OAM and SAM of optical states. We demonstrate the formation of vortex-antivortex structure and discuss interference of three vortex states in a BEC.