Topological Defects in Ferromagnetic, Antiferromagnetic and Cyclic Spinor Condensates -- A Homotopy Theory

Details Topological Defects in Ferromagnetic, Antiferromagnetic and Cyclic Spinor Condensates -- A Homotopy Theory Topological Defects in Ferromagnetic, Antiferromagnetic and Cyclic Spinor Condensates -- A Homotopy Theory

2004-04-06

arxiv.org/abs/cond-mat/0404138v1

Physics

Condensed Matter

Soft Condensed Matter

To appear in "Progress in Ferromagnetic Research", Frank Columbus, editor (Nova Science Publishers, New York, 2004) A continua

Scientific paper

We apply the homotopy group theory in classifying the topological defects in atomic spin-1 and spin-2 Bose-Einstein condensates. The nature of the defects depends crucially on the spin-spin interaction between the atoms. We find the topologically stable defects both for spin-1 ferromagnetic and anti-ferromagnetic states, and for spin-2 ferromagnetic and cyclic states. With this rigorous approach we clarify the previously controversial identification of symmetry groups and order parameter spaces for the spin-1 anti-ferromagnetic state, and show that the spin-2 cyclic case provides a rare example of a physical system with non-Abelian line defects, like those observed in biaxial nematics. We also show the possibility to produce vortices with fractional winding numbers of 1/2, 1/3 and their multiples in spinor condensates.

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