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Physica Scripta

SU(3) symmetry of spin-1 Bose–Einstein condensate

Tuguldur Begzjav, Duger Ulam-Orgikh

Published Jan 11, 2023• 0 citations
Publisher

Abstract

Abstract It is well-known that spin-1 atoms have SU(3) symmetry. In this work, we develop the theory for spin-1 Bose–Einstein condensate (BEC) based on SU(3) Lie group and predict that any spin-1 atom, for instance, 87Rb can exist in either of two inequivalent fundamental representations of SU(3) namely D(1, 0) or D(0, 1). Furthermore, the SU(3) theoretical treatment results in either ferromagnetic or antiferromagnetic ground states of the spin-1 BEC depending on the sign of a 1,1 − a 0,0, where a 1,1 and a 0,0 are the scattering lengths corresponding to D(1, 1) and D(0, 0) states. We also show that the coherent spin mixing process of spin-1 BEC is due to only the collisions between atoms in the D(1, 0) and D(0, 1) representations.

DOI
10.1088/1402-4896/acb243

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Abstract We study solitons in a spin-1 Bose–Einstein condensates with SU(3) spin–orbit coupling. We obtain the ground state and the metastable solution for solitons with attractive interactions by the imaginary-time evolution method. Compared with the SU(2) spin–orbit coupling, it is found that the solitons in SU (3) spin–orbit coupling show a new feature due to breaking the symmetry. The solitons called the composite solitons have mixing manifolds of ferromagnetic and antiferromagnetic states. This has stimulated people to study the topological excitation properties of SU (3) spin–orbit coupling and it is expected to find new quantum phases.
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We analyze quantum correlation properties of a spinor-1 (f=1)(f=1)(f=1) Bose-Einstein condensate using the Gell-Mann realization of SU(3) symmetry. We show that previously discussed phenomena of condensate fragmentation and spin mixing can be explained in terms of the hypercharge symmetry. The ground state of a spinor-1 condensate is found to be fragmented for ferromagnetic interactions. The notion of two-bosonic-mode squeezing is generalized to the two-spin $(U\ensuremath{-}V)$ squeezing within the SU(3) formalism. Spin squeezing in the isospin subspace (T) is found and is numerically investigated. We also provide results for the stationary states of spinor-1 condensates.
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Free and Harmonic Trapped Spin-1 Bose–Einstein Condensates in R3{{\mathbb{R}}^{3}}R3
Abstract. We investigate physical states of spin-1 Bose–Einstein condensate in [Formula: see text] with mean-field interaction constant [Formula: see text] and spin-exchange interaction constant [Formula: see text], two conserved quantities, the number of atoms [Formula: see text], and the total magnetization [Formula: see text] are involved in. First, in the free case, existence and asymptotic behavior of ground states are analyzed according to the relations among [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. Furthermore, we show that the corresponding standing wave is strongly unstable. When the atoms are trapped in a harmonic potential, we prove the existence of ground states and excited states along with some precisely asymptotics. Besides, we get that the set of ground states is stable under the associated Cauchy flow while the excited state corresponds to a strongly unstable standing wave. Our results not only show some characteristics of three-dimensional spin-1 BEC under the effect between the spin-dependent interaction and the external magnetic field, but also support some experimental observations as well as numerical results on spin-1 BEC.