Acoustic superradiance from an optical-superradiance-induced vortex in a Bose-Einstein condensate

We consider the simultaneous scattering of an angular momentum carrying Laguerre-Gaussian light beam and an acoustic wave from an atomic Bose-Einstein condensate, under condition of optical superradiance induced vortex state. 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 spacetime. 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 simultaneously leads to the optical and acoustic superradiance.