Classifying Novel Phases of Spinor Atoms

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. Such states include BEC phases and insulating Mott states with one atom per site. We describe and apply a classification scheme that makes explicit 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. After discussing the general formalism we apply it to the many-body states of bosons with hyperfine 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: the hexagon, the pyramid with pentagonal base, the prism, and the octahedron.

Added references, corrected typos, minor changes in text

References in corpus (6)

• Bose-Einstein condensation of chromium
• Implementation of Spin Hamiltonians in Optical Lattices
• Coherent collisional spin dynamics in optical lattices
• Dynamics of F=1 87Rb condensates at finite temperatures
• Bose-Einstein condensation of trapped interacting spin-1 atoms
• Quantum insulating states of F=2 cold atoms in optical lattices

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• Ground-state phase diagram and magnetic properties of a tetramerized spin-1/2 J_1-J_2 model: BEC of bound magnons and absence of the transverse magnetization
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• Competing Orders in One-Dimensional Half-Integer Fermionic Cold Atoms: A Conformal Field Theory Approach
• Heteronuclear fermionic superfluids with spin degrees of freedom
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• Resonant spin-changing collisions in spinor Fermi gases
• Excited state spectra at the superfluid-insulator transition out of paired condensates