Abstract
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.
Highlights
Analogies in physics enable us to observe a particular phenomenon with the same characteristic features in different systems pertaining to disparate mechanisms and space-time-energy scales
A particular example is the analogy between a cosmic black hole and the microscopic vortex state of a Bose-Einstein condensate, which casts the superradiance phenomenon of scalar waves from the black hole to the superradiance of acoustic waves from the liquid vortex
The time domain solutions are obtained by solving the Klein-Gordon equation for the propagation of acoustic waves, whereas the spectral analysis of the superradiance is conducted by asymptotic solutions of the waves at the event horizon and the spatial infinity
Summary
Analogies in physics enable us to observe a particular phenomenon with the same characteristic features in different systems pertaining to disparate mechanisms and space-time-energy scales. Since observing a cosmic scale superradiance is not a feasible option [3], we currently rely on analogous systems that can be realized at the laboratory scale In this case a 2 + 1 space-time geometry Kerr black hole [4, 5, 6]. The present work aims to contribute in two aspects: Providing a consolidating study of the temporal and spatial features of the scattering from a BEC vortex with constant background density and characterization of the superradiance as a function of the rotational speed of the vortex. The time domain solutions are obtained by solving the Klein-Gordon equation for the propagation of acoustic waves, whereas the spectral analysis of the superradiance is conducted by asymptotic solutions of the waves at the event horizon and the spatial infinity.
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