Skyrmion in spinor condensates and its stability in trap potentials

TL;DR

This paper investigates the existence and local stability of skyrmions in two-component Bose-Einstein condensates with SU(2) symmetry, identifying critical dissipation levels and minimum boson numbers needed for stable skyrmions.

Contribution

It extends previous work by analyzing the stability conditions and critical dissipation thresholds for skyrmions in spinor condensates with trap potentials.

Findings

Existence of a critical dissipation strength for skyrmions

A stability condition based on the ground-state energy of a quantum Hamiltonian

Minimum boson number for stable skyrmions can be as low as ~10^4

Abstract

A necessary condition for the existence of a skyrmion in two-component Bose-Einstein condensates with $\mathrm{SU(2)}$ symmetry was recently provided by two of the authors [Phys. Rev. Lett. {\bf 97}, 080403 (2006)], by mapping the problem to a classical particle in a potential subject to time-dependent dissipation. Here we further elaborate this approach. For two classes of models, we demonstrate the existence of the critical dissipation strength above which the skyrmion solution does not exist. Furthermore, we discuss the local stability of the skyrmion solution by considering the second-order variation. A sufficient condition for the local stability is given in terms of the ground-state energy of a one-dimensional quantum-mechanical Hamiltonian. This condition requires a minimum number of bosons, for a certain class of the trap potential. In the optimal case, the minimum number of bosons can be as small $\sim 10^4$.