Dissipative flow and vortex shedding in the Painlev\'e boundary layer of a Bose Einstein condensate

TL;DR

This paper investigates the origin of the critical velocity for vortex shedding in a Bose-Einstein condensate near its boundary layer, revealing that vortex shedding begins only after surpassing a specific threshold velocity.

Contribution

It provides a theoretical analysis of vortex shedding and critical velocity near the boundary layer of a BEC using Painlevé equations, highlighting differences from the center of the cloud.

Findings

Vortex shedding starts only above a threshold velocity.

Drag increases sharply at the onset of vortex shedding.

Critical velocity in the boundary layer is lower than in the center.

Abstract

Raman et al. have found experimental evidence for a critical velocity under which there is no dissipation when a detuned laser beam is moved in a Bose-Einstein condensate. We analyze the origin of this critical velocity in the low density region close to the boundary layer of the cloud. In the frame of the laser beam, we do a blow up on this low density region which can be described by a Painlev\'e equation and write the approximate equation satisfied by the wave function in this region. We find that there is always a drag around the laser beam. Though the beam passes through the surface of the cloud and the sound velocity is small in the Painlev\'e boundary layer, the shedding of vortices starts only when a threshold velocity is reached. This critical velocity is lower than the critical velocity computed for the corresponding 2D problem at the center of the cloud. At low velocity, there is a stationary solution without vortex and the drag is small. At the onset of vortex shedding, that is above the critical velocity, there is a drastic increase in drag.