Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2008-12-15
Phys. Rev. A 79, 053626 (2009)
Physics
Condensed Matter
Other Condensed Matter
12 pages, 9 figures, final version
Scientific paper
10.1103/PhysRevA.79.053626
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 $\sim 10^4$.
Herbut Igor F.
Mitamura Yohei
Oshikawa Masaki
Tokuno Akiyuki
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