Analog Black Holes and Energy Extraction by Super-Radiance from Bose Einstein Condensates (BEC) with Constant Density

TL;DR

This study numerically investigates acoustic superradiance in a Bose-Einstein condensate vortex, demonstrating energy extraction analogous to black hole superradiance through detailed spectral and dynamical analysis.

Contribution

It introduces a coordinate transformation method to identify horizons in BEC vortices and provides a comprehensive analysis of superradiance effects using both time-domain and spectral approaches.

Findings

Good agreement between dynamical and spectral results

Identification of event horizon and ergosphere in BEC vortex

Frequency spectrum of superradiance as a function of vortex rotation

Abstract

This paper presents a numerical study of the acoustic superradiance from the single vortex state of a Bose-Einstein condensate (BEC). The draining bathtub model of an incompressible barotropic fluid is adopted to describe the vortex. The propagation of the velocity potential fluctuations 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. Particular to this study, a coordinate transformation is applied which enables the identification of the event horizon and the ergosphere termwise in the metric. Thus, the respective spectral solutions can be obtained asymptotically at either boundary. Further, the time-domain calculations of the energy of the propagating perturbations and the independently performed reflection coefficient calculations from the asymptotic solutions of the propagating perturbations are shown to be in very good agreement. While the former solution provides the full dynamical behavior of the superradiance, the latter method gives the frequency spectrum of the superradiance as a function of the rotational frequency of the vortex. Hence, a comprehensive analysis of the superradiance effect can be conducted within this workframe.