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arXiv:cond-mat/0504398 · Physical Review A

Spontaneous magnetization and structure formation in a spin-1 ferromagnetic Bose-Einstein condensate

Hiroki Saito, Masahito Ueda

Published Aug 16, 2005• 68 citations
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Abstract

Motivated by recent experiments involving the nondestructive imaging of magnetization of a spin-1 $^{87}\mathrm{Rb}$ Bose gas [J. M. Higbie et al., Phys. Rev. Lett., 95, 050401 (2005)], we address the question of how the spontaneous magnetization of a ferromagnetic Bose-Einstein condensate occurs in a spin-conserving system. Due to competition between the ferromagnetic interaction and the total spin conservation, various spin structures such as staggered magnetic domains and helical and concentric ring structures are formed, depending on the geometry of the trapping potential.

DOI
10.1103/physreva.72.023610

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Motivated by recent experiments involving the nondestructive imaging of magnetization of a spin-1 87Rb^{87}\mathrm{Rb}87Rb Bose gas [J. M. Higbie et al., Phys. Rev. Lett., 95, 050401 (2005)], we address the question of how the spontaneous magnetization of a ferromagnetic Bose-Einstein condensate occurs in a spin-conserving system. Due to competition between the ferromagnetic interaction and the total spin conservation, various spin structures such as staggered magnetic domains and helical and concentric ring structures are formed, depending on the geometry of the trapping potential.
We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.
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We investigate Bose-Einstein condensation of trapped spin-1 atoms with ferromagnetic or antiferromagnetic two-body contact interactions. We adopt the mean field theory and develop a Hartree-Fock-Popov type approximation in terms of a semiclassical two-fluid model. For antiferromagnetic interactions, our study reveals double condensations as atoms in the $\ensuremath{\mid}{m}_{F}=0⟩$ state never seem to condense under the constraints of both the conservation of total atom number NNN and magnetization MMM. For ferromagnetic interactions, however, triple condensations can occur. Our results can be conveniently understood in terms of the interplay of three factors: (anti)ferromagnetic atom-atom interactions, MMM conservation, and the miscibilities between and among different condensed components.
We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature Tc{T}_{c}Tc​. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below Tc{T}_{c}Tc​ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.