利用偶极-偶极相互作用稳定二维孤子的魔倾角
A magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions
摘要：
在Gross-Pitaevskii方程的框架下，研究了偶极玻色-爱因斯坦凝聚体（BEC）中有效二维孤子的形成和稳定性，其中偶极矩相对于系统平面的法线方向成任意角度$θ$.利用数值方法和变分近似，我们证明了在$θ^{\text{cr}}<θ\leq π/2$区间内，偶极-偶极相互作用（DDI）可以使接触吸引相互作用产生的不稳定的Townes孤子完全稳定（具有各向异性的形状）.稳定性边界$θ^{\text{cr}}$弱依赖于DDI的相对强度，保持接近“魔角”$θ_{m}=\arccos \left( 1/\sqrt{3}\right) $。结果表明，DDI提供了一个通用的机制，在更高的维度稳定的BEC\孤子的创建。
英文摘要：
In the framework of the Gross-Pitaevskii equation, we study the formation and stability of effectively two-dimensional solitons in dipolar Bose-Einstein condensates (BECs), with dipole moments polarized at an arbitrary angle $θ$ relative to the direction normal to the system's plane. Using numerical methods and the variational approximation, we demonstrate that unstable Townes solitons, created by the contact attractive interaction, may be completely stabilized (with an anisotropic shape) by the dipole-dipole interaction (DDI), in interval $θ^{\text{cr}}<θ\leq π/2$. The stability boundary, $θ^{\text{cr}}$, weakly depends on the relative strength of DDI, remaining close to the "magic angle", $θ_{m}=\arccos \left( 1/\sqrt{3}\right) $. The results suggest that DDIs provide a generic mechanism for the creation of stable BEC\ solitons in higher dimensions.
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