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arXiv:1605.02864 · Physical Review A

Magnetic-field-induced dynamical instabilities in an antiferromagnetic spin-1 Bose-Einstein condensate

Zhengguo Pu, Jun Zhang, Su Yi, Dajun Wang, Wenxian Zhang

Published May 31, 2016• 9 citations
arXivHTMLPDF

Abstract

We theoretically investigate four types of dynamical instability, in particular the periodic and oscillatory type ${I}_{O}$, in an antiferromagnetic spin-1 Bose-Einstein condensate in a nonzero magnetic field, by employing the coupled-mode theory and numerical method. This is in sharp contrast to the dynamical stability of the same system in zero field. Remarkably, a pattern transition from a periodic dynamical instability ${I}_{O}$ to a uniform one ${\mathit{\text{III}}}_{O}$ occurs at a critical magnetic field. All four types of dynamical instability and the pattern transition are ready to be detected in $^{23}\mathrm{Na}$ condensates within the availability of the current experimental techniques.

DOI
10.1103/physreva.93.053628

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We show that metastable phases of an antiferromagnetic spin-1 condensate in a simple model with pure contact interactions can exhibit a rotonlike minimum in the excitation spectrum. The introduction of a magnetic field gives rise to the instability of roton modes, which can lead to spontaneous emergence of regular periodic, polygonal, polyhedral, or crystalline patterns, as shown in numerical simulations within the truncated Wigner approximation. An explanation of the occurrence of rotonlike instability is given based on the energy and spin conservation laws.
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Antiferromagnetic condensates are generally believed not to display modulational instability and subsequent spin-domain formation. Here we demonstrate that in the presence of a homogeneous magnetic field antiferromagnetic spin-1 Bose-Einstein condensates can undergo spatial modulational instability followed by the subsequent generation of spin domains. Employing numerical simulations for realistic conditions, we show how this effect can be observed in sodium condensates confined in an optical trap. Finally, we link this instability and spin-domain formation with stationary modes of the condensate.
We analyze the structure of spin-one Bose-Einstein condensates in the presence of a homogeneous magnetic field. We classify the homogeneous stationary states and study their existence, bifurcations, and energy spectra. We reveal that phase separation can occur in the ground state of antiferromagnetic (polar) condensates while the spin components of the ferromagnetic condensates are always miscible and no phase separation occurs. Our theoretical model, confirmed by numerical simulations, explains that this phenomenon takes place when the energy of the lowest homogeneous state is a concave function of the magnetization. In particular, we predict that phase separation can be observed in a 23Na^{23}\text{N}\text{a}23Na condensate confined in a highly elongated harmonic trap. Finally, we discuss the phenomena of dynamical instability and spin domain formation.