Superfluid flow past an obstacle in annular Bose--Einstein condensates

TL;DR

This paper studies superfluid flow in ring-shaped Bose--Einstein condensates, revealing multiple critical velocities, bifurcations, and persistent currents through analysis of nonlinear Schrödinger equations with periodic boundary conditions.

Contribution

It introduces the analysis of multiple critical velocities and bifurcation structures in superfluid flow in annular Bose--Einstein condensates, extending understanding beyond infinite domain cases.

Findings

Multiple critical velocities identified for superfluid flow.

Bifurcation diagram shows saddle-center bifurcations leading to circulation changes.

Unstable solutions exhibit complex dynamics and instabilities.

Abstract

We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities, localized solutions with a nontrivial phase profile appear. In striking difference from the infinite domain, in this case there are many critical velocities. At each critical velocity, the steady flow solutions disappear in a saddle-center bifurcation. These interconnected branches of the bifurcation diagram lead to additions of circulation quanta to the phase of the associated solution. This, in turn, relates to the manifestation of persistent current in numerous recent experimental and theoretical works, the connections to which we touch upon. The complex dynamics of the identified waveforms and the instability of unstable solution branches are demonstrated.