Critical Rotational Speeds for Superfluids in Homogeneous Traps

TL;DR

This paper analyzes the effects of rapid rotation on superfluids in homogeneous traps, identifying three critical speeds for vortex formation, hole creation, and giant vortex emergence, highlighting differences from flat trap models.

Contribution

It introduces a new asymptotic analysis for superfluids in soft, homogeneous traps, revealing distinct behaviors and regimes compared to flat traps, especially near the giant vortex transition.

Findings

Identified three critical rotational velocities for vortex phenomena.

Discovered the Gaussian profile of the superfluid near the giant vortex transition.

Highlighted differences in vortex size and bulk profile between soft and flat traps.

Abstract

We present an asymptotic analysis of the effects of rapid rotation on the ground state properties of a superfluid confined in a two-dimensional trap. The trapping potential is assumed to be radial and homogeneous of degree larger than two in addition to a quadratic term. Three critical rotational velocities are identified, marking respectively the first appearance of vortices, the creation of a `hole' of low density within a vortex lattice, and the emergence of a giant vortex state free of vortices in the bulk. These phenomena have previously been established rigorously for a `flat' trap with fixed boundary but the `soft' traps considered in the present paper exhibit some significant differences, in particular the giant vortex regime, that necessitate a new approach. These differences concern both the shape of the bulk profile and the size of vortices relative to the width of the annulus where the bulk of the superfluid resides. Close to the giant vortex transition the profile is of Thomas-Fermi type in `flat' traps, whereas it is gaussian for soft traps, and the `last' vortices to survive in the bulk before the giant vortex transition are small relative to the width of the annulus in the former case but of comparable size in the latter.