Acoustic superradiance from a Bose–Einstein condensate vortex with a self-consistent background density profile

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.