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Physical review. B, Condensed matter

Wave acoustics for propagation of ultrasound along a vortex array in superfluid A3

Edouard B Sonin, Kenji Torizuka, Jukka M. Kyynarainen, Jukka P Pekola, George Tvalashvili

Published May 1, 1992• 44 citations
Publisher

Abstract

A wave-acoustics theory has been developed to describe the propagation of zero sound parallel to vortex lines in rotating $^{3}\mathit{A}$. We show that a diffraction ``shadow'' is formed in which the wave amplitude is suppressed by interference around vortices. This phenomenon contributes to the experimentally observed effect of rotation on the sound amplitude and exceeds the attenuation at large core radii. The dependence of the diffraction contribution on the angular velocity changes drastically at the transition from vortices with a finite core to coreless vortices when the magnetic field is decreased to zero. We derive conditions for the applicability of the effective-medium theory and the classical geometrical acoustic method in describing sound propagation along vortices.

DOI
10.1103/physrevb.45.10536

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Rotation of superfluid 3B^{3}\mathit{B}3B in an magnetic field enhances the coupling of the nonzero mJ{\mathrm{m}}_{\mathrm{J}}mJ​ substrates of the real squashing collective mode to the zero sound, and the fivefold line splitting becomes observable even when H is parallel to \ensuremath{\Omega} and to the direction of sound propagation. Equilibrium vortex lattices and vortex-free states can be distinguished by their characteristic absorption spectra. The dependence of the sound attenuation on the angular velocity in magnetic fields up to 32 mT is reported; the data are qualitatively compared with theory.
We present a systematic derivation of the effective action for interacting vortices in a nonrelativistic two-dimensional superfluid described by the Gross-Pitaevskii equation by integrating out longitudinal fluctuations of the order parameter. There are no logarithmically divergent coefficients in the equations of motion. Our analysis is valid in a dilute limit of vortices where the intervortex spacing is large compared to the core size, and where number fluctuations of atoms in vortex cores are suppressed. We analyze sound-induced corrections to the dynamics of a vortex-antivortex pair and show that there is no instability to annihilation, suggesting that sound-mediated interactions are not strong enough to ruin an inverse energy cascade in two-dimensional zero-temperature superfluid turbulence.
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.
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.
The scattering of plane acoustic waves by a vortex in a two-dimensional superfluid is examined for small Mach number M . The solution is developed from a systematic expansion of the governing equations in three separate regions: an inner vortical region which scales as the healing length, an interaction region governed by irrotational hydrodynamics and an outer wave region. The solutions in the different regions are matched together. The leading-order scattered field occurs at O( M 2 δ) in the wave region, where δ is the small non-dimensional amplitude of the incoming acoustic wave. The far-field behaviour of the wave-region solution shows that a different form of the expansion is required in the forward scatter direction: this corresponds to the expression previously derived for the acoustic Magnus force.