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arXiv:cond-mat/0201507 · Physical Review A

Axisymmetric vortices in spinor Bose-Einstein condensates under rotation

Tomoya Isoshima, Kazushige Machida

Published Aug 5, 2002• 59 citations
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Abstract

The relative stability of various axisymmetric vortices in a spinor Bose-Einstein condensate with $F=1$ 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.

DOI
10.1103/physreva.66.023602

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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.
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.
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.
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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.
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations coupled with the Gross-Pitavskii equation, the elementary excitations and the total energy of the systems are calculated as a function of rotation velocity. There are two distinct criteria of vortex stability; The position of the excitation energy levels relative to the condensate energy level yields the local stability criterion, and the total energy relative to that of the non-vortex state yields the global stability criterion. The vortex stability phase diagram in the rotation velocity vs the particle density of the system is obtained, allowing one to locate the appropriate region to observe the singly quantized vortex.
We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F(z)=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin |<S-->>| to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.