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arXiv:1109.0400 · Physical Review A

Symmetry classification of spinor Bose-Einstein condensates

Yuki Kawaguchi, Masahito Ueda

Published Nov 15, 2011• 69 citations
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Abstract

We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing the symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a noninert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2, and 3 cases at zero magnetic field, and find an additional phase in the last case. The properties of the vortices in the spin-3 system are also discussed.

DOI
10.1103/physreva.84.053616

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We propose a method for systematically finding ground states of spinor Bose-Einstein condensates by utilizing the symmetry properties of the system. By this method, we can find not only an inert state, whose symmetry is maximal in the manifold under consideration, but also a noninert state, which has lower symmetry and depends on the parameters in the Hamiltonian. We establish the symmetry-classification method for the spin-1, 2, and 3 cases at zero magnetic field, and find an additional phase in the last case. The properties of the vortices in the spin-3 system are also discussed.
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This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S 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.
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.
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.