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arXiv:cond-mat/0404138

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

Yunbo Zhang, H. Mäkelä, Kalle‐Antti Suominen

Published Apr 6, 2004• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0404138

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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.
We investigate the structure of topological defects in the ground states of spinor Bose–Einstein condensates with spin F = 1 or F = 2. The type and number of defects are determined by calculating the first and second homotopy groups of the order-parameter space. The order-parameter space is identified with a set of degenerate ground state spinors. Because the structure of the ground state depends on whether or not there is an external magnetic field applied to the system, defects are sensitive to the magnetic field. We study both cases and find that the defects in zero and non-zero field are different.
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In this paper we first derive a general method which enables one to create expressions for vortices and monopoles. By using this method we construct several order-parameters describing the vortices and monopoles of Bose–Einstein condensates with hyperfine spin F = 1 and F = 2. We concentrate on defects which are topologically stable in the absence of an external magnetic field. In particular we show that in a ferromagnetic condensate there can be a vortex which does produce any superfluid flow. We also point out that the order-parameter space of the cyclic phase of F = 2 condensate consists of two disconnected sets. Finally we examine the effect of an external magnetic field on the vortices of a ferromagnetic F = 1 condensate and discuss the experimental preparation of a vortex in this system.