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arXiv:cond-mat/0208032 · Physical Review A

Axisymmetric versus nonaxisymmetric vortices in spinor Bose-Einstein condensates

Takeshi Mizushima, K. Machida, Takafumi Kita

Published Nov 12, 2002• 70 citations
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Abstract

The structure and stability of various vortices in $F=1$ spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both axisymmetric and nonaxisymmetric vortices and covering a wide range of ferromagnetic and antiferromagnetic interactions. The topological defect called the Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for the ferromagnetic case. The phase diagram is established in a plane of external rotation $\ensuremath{\Omega}$ versus total magnetization M by comparing the free energies of possible vortices. It is shown that there are qualitative differences between axisymmetric and nonaxisymmetric vortices which are manifested in the $\ensuremath{\Omega}$ and M dependences.

DOI
10.1103/physreva.66.053610

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The structure and stability of various vortices in F=1F=1F=1 spinor Bose-Einstein condensates are investigated by solving the extended Gross-Pitaevskii equation under rotation. We perform an extensive search for stable vortices, considering both axisymmetric and nonaxisymmetric vortices and covering a wide range of ferromagnetic and antiferromagnetic interactions. The topological defect called the Mermin-Ho (Anderson-Toulouse) vortex is shown to be stable for the ferromagnetic case. The phase diagram is established in a plane of external rotation \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ versus total magnetization M by comparing the free energies of possible vortices. It is shown that there are qualitative differences between axisymmetric and nonaxisymmetric vortices which are manifested in the \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ and M dependences.
The relative stability of various axisymmetric vortices in a spinor Bose-Einstein condensate with F=1F=1F=1 is examined within extended Bogoliubov theory. This yields the phase diagram in the plane of external rotation frequency vs magnetization. We compare antiferromagnetic, nonmagnetic, and ferromagnetic cases. The excitation spectrum is evaluated under rotation to investigate the local stability of the possible vortices and the vortex nucleation frequency.
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The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along the z axis and comparing the energies of other competing non-axis-symmetric or singular vortices. The phase diagram is thereby established in a plane of the rotation drive vs the total magnetization. Their stability is also checked by calculating collective modes based on the Bogoliubov equations.
We investigate the dynamical stability of the coreless vortex state in F = 1 spinor Bose-Einstein condensates, by numerically solving the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We cover both ferromagnetic and antiferromagnetic interaction regions and the magnetizations per particle M from -1 to +1. It is found that the coreless vortex state is dynamically stable in large parameter regions of magnetization M . At M = -1, the hyperfine spin component with vortex winding 2 is dominant, and hence the coreless vortex can spontaneously decay even without dissipation. However, it is found that in the ferromagnetic case, the spin-spin interactions tend to stabilize the state. In the antiferromagnetic case, we find new dynamical instability modes which are not obtained in the ferromagnetic interaction region. In the antiferromagnetic interaction region, the spin-spin interactions can stimulate dynamical instabilities, while there still remains a large stability area in the parameter M . This is because of certain restrictions in inducing dynamical instability.
Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin F=1F=1F=1 are investigated theoretically based on the Ginzburg-Pitaevskii equations near Tc.{T}_{c}.Tc​. The Abrikosov lattice with clear core regions is never found to be stable at any rotation drive $\ensuremath{\Omega}.$ Instead, each component ${\ensuremath{\Psi}}_{i}(i=0,\ifmmode\pm\else\textpm\fi{}1)$ prefers to shift the core locations away from the others to realize almost uniform order-parameter amplitude with complicated magnetic-moment configurations. This system is characterized by many competing metastable structures so that quite a variety of vortices may be realized with a small change in external parameters.
We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.