Echoes From the Event Horizon of a Superfluid Vortex

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.