Topological classification of vortex-core structures of spin-1 Bose-Einstein condensates

Abstract

We classify vortex-core structures according to the topology of the order parameter space. We develop a method to characterize how the order parameter changes inside the vortex core. We apply it to spin-1 Bose-Einstein condensates and show that the vortex-core structures are classified by winding numbers that are locally defined in the core region. We also show that a vortex-core structure with a nontrivial winding number can be stabilized under a negative quadratic Zeeman effect.

Dynamics of a vortex dipole across a magnetic phase boundary in a spinor Bose-Einstein condensate

“…From a topological point of view, in general, vortex states in the ferromagnetic phase, classified by π 1 (G f ) = Z 2 , and those in the polar phase, classified by π 1 (G p ) = Z, can be smoothly connected to each other [19]. In fact, spin states far from the core may be transformed from the ferromagnetic phase to the polar phase as…”

“…The radial functions f f (r), f (14), which corresponds to Fig. 5(f), the spin state has the form of ∝ (e ±iθ , 0, 1) T for a radius r ∼ ξ s satisfying f f (r) ≃ f core f (r), which is a half-quantum vortex [19]. Thus, the vortex dipole in the ferromagnetic phase shown in Fig.…”

“…In a BEC of atoms with spin degrees of freedom, the ground-state manifold has a more complicated topology, and a variety of spin vortices exist, such as a half-quantum vortex [3] and a polar-core vortex [4]. Topological properties of spinor BECs have been studied by many researchers [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…In Ref. [19], structures of spinvortex cores were studied. This problem is also regarded as the spin-vortex connection between different phases, since the symmetry group of the spin state changes radially from infinity to the vortex core.…”

Stability and internal structure of vortices in spin-1 Bose-Einstein condensates with conserved magnetization

“…To avoid depletion of the atom density, F (ρ) may then increase back to F (ρ → 0) = 1 inside the core of the half-quantum vortex, corresponding to the vortex-free FM phase. A similar composite vortex state was considered in a recent topological classifications of vortex cores in spin-1 BECs [27].…”