Vortex-Induced Phase Slip Dissipation in a Toroidal Bose-Einstein Condensate Flowing Through a Barrier

We study superfluid dissipation due to phase slips for a BEC flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus while the condensate flows with a finite quantized angular momentum. At a critical height, a vortex moves from the inner region and reaches the barrier to eventually circulate around the annulus. At a higher critical height, an anti-vortex also enters into the torus from the outer region. Both vortex and anti-vortex decrease the total angular momentum by leaving behind a $2\pi$ phase slip. When they collide and annihilate or orbit along the same loop, the condensate suffers a global $2\pi$ phase slip, and the total angular momentum decreases by one quantum. In hydrodynamic regime, the instability sets in when the local superfluid velocity equals the sound speed inside the barrier region.