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arXiv:cond-mat/0607253 · Physical Review Letters

Classifying Novel Phases of Spinor Atoms

Ryan Barnett, Ari M. Turner, Eugene Demler

Published Nov 3, 2006• 144 citations
arXivHTMLPDF

Abstract

We consider many-body states of bosonic spinor atoms which, at the mean-field level, can be characterized by a single-particle wave function for the Bose-Einstein condensation and Mott insulating states. We describe and apply a classification scheme that makes explicit the spin symmetries of such states and enables one to naturally analyze their collective modes and topological excitations. Quite generally, the method allows classification of a spin F system as a polyhedron with 2F vertices. We apply the method to the many-body states of bosons with spins two and three. For spin-two atoms we find the ferromagnetic state, a continuum of nematic states, and a state having the symmetry of the point group of the regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and nematic phases as well as states having symmetries of various types of polyhedra with six vertices.

DOI
10.1103/physrevlett.97.180412

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We develop a symmetry classification scheme to find ground states of pseudo-spin-12\frac{1}{2}21​, spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin-12\frac{1}{2}21​ condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin-12\frac{1}{2}21​ system, although mean-field states always break time-reversal symmetry, there exists a time-reversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.
Motivated by the recent realization of a 52Cr^{52}\mathrm{Cr}52Cr Bose-Einstein condensate, we consider the phase diagram of a general spin-three condensate as a function of its scattering lengths. We classify each phase according to its reciprocal spinor, using a method developed in a previous work. We show that such a classification can be naturally extended to describe the vortices for a spinor condensate by using the topological theory of defects. To illustrate, we systematically describe the types of vortex excitations for each phase of the spin-three condensate.
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