Skyrmion in spinor condensates and its stability in trap potentials

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 $\sim 10^4$.

12 pages, 9 figures, final version

References in corpus (13)

• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Vortices in multicomponent Bose-Einstein condensates
• QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid
• Competing orders, non-linear sigma models, and topological terms in quantum magnets
• QED3 theory of underdoped high temperature superconductors
• Antiferromagnetism from phase disordering of a d-wave superconductor
• Polarization of interacting bosons with spin
• Charge modulation, spin response, and dual Hofstadter butterfly in high-Tc cuprates
• Effective theory of high-temperature superconductors
• Stable Skyrmions in spinor condensates
• Saturated Ferromagnetism from Statistical Transmutation in Two Dimensions
• The role of point-like topological excitations at criticality: from vortices to global monopoles
• Are there static texture?

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• Matryoshka Skyrmions
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• Incarnations of Skyrmions
• Wall-vortex composite solitons in two-component Bose-Einstein condensates
• Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin-orbit coupling in an optical lattice
• Baryonic torii: Toroidal baryons in a generalized Skyrme model
• Symmetry protected skyrmions in 3D spin-orbit coupled Bose gases
• Baryonic handles: Skyrmions as open vortex strings on a domain wall
• Linked vortices as baryons in the miscible BEC-Skyrme model
• Hydrodynamic generation of skyrmions in a two-component Bose-Einstein condensate
• Experimental and Theoretical Evidence for Extended Particle Models