Interplay between phonons and vorticity in a rotating superfluid

In a superfluid system, phonons are collective excitations that propagate as sound waves, experiencing an effective curved spacetime due to the background density of the Bose-Einstein condensate (BEC). Quantized flow around a hole in a 2D box can be realized by imprinting a vortex phase on the atomic BEC. Such a background flow has a similarity with the Kerr spacetime around a rotating black hole. We study the effect of this rotational flow on the phonons excited in the box. One interesting aspect of the rotational flow is the coupling of different orthogonal phonon modes of the box. We further examine how large amplitude phonons perturb the quantized flow, unveiling the interplay between collective excitations and superfluid vorticity.