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arXiv:cond-mat/0204025 · Physical Review A

Spinor Bose-Einstein condensates with many vortices

Takafumi Kita, Takeshi Mizushima, K. Machida

Published Dec 18, 2002• 34 citations
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Abstract

Vortex-lattice structures of antiferromagnetic spinor Bose-Einstein condensates with hyperfine spin $F=1$ are investigated theoretically based on the Ginzburg-Pitaevskii equations near ${T}_{c}.$ 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.

DOI
10.1103/physreva.66.061601

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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 \ensuremathΩ.\ensuremath{\Omega}.\ensuremathΩ. Instead, each component \ensuremathΨi(i=0,\ifmmode±\else\textpm\fi1){\ensuremath{\Psi}}_{i}(i=0,\ifmmode\pm\else\textpm\fi{}1)\ensuremathΨi​(i=0,\ifmmode±\else\textpm\fi1) 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 theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC's) with a ferromagnetic spin interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multicomponent order parameters, such as Mermin-Ho and Anderson-Toulouse coreless vortices (the two-dimensional Skyrmion and meron) and nonaxisymmetric vortices with shifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of an external magnetic field. In addition, the vortex phase diagram is constructed in the plane of the total magnetization MMM and the external rotation frequency $\ensuremath{\Omega}$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagrams in the $M\text{\ensuremath{-}}\ensuremath{\Omega}$ plane may be divided into two categories: (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms composite lattices of coreless and polar-core vortices. The difference between type (i) and type (ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discuss the stability of triangular and square lattice states for rapidly rotating condensates.
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 $\ensuremath{\Omega}$ 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.
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.
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.
Quantum vortices in the multi-component Bose-Einstein condensation (BEC) are investigated theoretically. It is found that three kinds of the vortex configurations are possible and their physical properties are discussed in details, including the density distribution and the spin texture. By using the Bogoliubov theory extended to the three component BEC, the collective modes for these vortices are evaluated. The local vortex stability for these vortices are examined in light of the existence of the negative eigenvalue, yielding a narrow magnetization window for the local intrinsic stable region where the multi-components work together to stabilize a vortex in a self-organized way.