Yi Li, Xiangfa Zhou, Congjun Wu
We study the unconventional condensation of the two-component bosons in a harmonic trap subject to the 3D $\vec{\sigma}\cdot \vec{p}$-type spin-orbit (SO) coupling. The topology of condensate wavefunctions explicitly manifests in the quaternionic representation, exhibiting skyrmion configurations for the mapping from the coordinate space to the quaternionic phase space $S^3$. The spin density distributions map the coordinate space to the $S^2$ Bloch sphere with non-zero Hopf invariants. As increasing SO coupling strength, spin textures evolve from concentric distributions to lattice structures at weak interactions. Strong interactions change condensates into spin-polarized plane-wave states, or, superpositions of two plane-waves exhibiting helical spin spirals.
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http://arxiv.org/abs/1205.2162
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