Coreless and singular vortex lattices in rotating spinor Bose-Einstein condensates

摘要

We theoretically investigate vortex-lattice phases of rotating spinorBose-Einstein condensates (BEC) with the ferromagnetic spin-interaction bynumerically solving the Gross-Pitaevskii equation. The spinor BEC under slowrotation can sustain a rich variety of exotic vortices due to themulti-component order parameters, such as the Mermin-Ho and Anderson-Toulousecoreless vortices (the 2-dimensional skyrmion and meron) and thenon-axisymmetric vortices with the sifting vortex cores. Here, we present thespin texture of various vortex-lattice states at higher rotation rates and inthe presence of the external magnetic field. In addition, the vortex phasediagram is constructed in the plane by the total magnetization $M$ and theexternal rotation frequency $\Omega$ by comparing the free energies of possiblevortices. It is shown that the vortex phase diagram in a $M$-$\Omega$ plane maybe divided into two categories; (i) the coreless vortex lattice formed by theseveral types of Mermin-Ho vortices and (ii) the vortex lattice filling in thecores with the pure polar (antiferromagnetic) state. In particular, it is foundthat the type-(ii) state forms the composite lattices of coreless andpolar-core vortices. The difference between the type-(i) and type-(ii) resultsfrom the existence of the singularity of the spin textures, which may beexperimentally confirmed by the spin imaging within polarized light recentlyproposed by Carusotto and Mueller. We also discussed on the stability oftriangular and square lattice states for rapidly rotating condensates.