Vortex Phases of Rotating Superfluids

TL;DR

This paper provides the first rigorous mathematical proof of a transition to a giant vortex state in rotating superfluids within anharmonic traps, revealing differences based on trap types and symmetry breaking in the ground state.

Contribution

It offers the first rigorous analysis of vortex transitions in rotating superfluids using Gross-Pitaevskii theory, highlighting differences between trap types and symmetry properties.

Findings

Vortex transition to giant vortex state proven mathematically.

Differences in vortex behavior between soft and fixed boundary traps.

Symmetry breaking in the ground state density profile.

Abstract

We report on the first mathematically rigorous proofs of a transition to a giant vortex state of a superfluid in rotating anharmonic traps. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and large rotational velocity and is based on precise asymptotic estimates on the ground state energy. An interesting aspect is a significant difference between 'soft' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary. In the former case vortices persist in the bulk until the width of the annulus becomes comparable to the size of the vortex cores. In the second case the transition already takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus. Moreover, the density profiles in the annulus are different in the two cases. In both cases rotational symmetry of the density in a true ground state is broken, even though a symmetric variational ansatz gives an excellent approximation to the energy.