A magic tilt angle for stabilizing two-dimensional solitons by dipole-dipole interactions

Abstract

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 $\theta$ 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 ${\theta }^{\text{cr}}<\theta \le \pi /2$. The stability boundary, ${\theta }^{\text{cr}}$, weakly depends on the relative strength of DDI, remaining close to the "magic angle", ${\theta }_m=\arccos \left(1/\sqrt{3}\right)$. The results suggest that DDIs provide a generic mechanism for the creation of stable BEC\ solitons in higher dimensions.

9 pages, 7 figures; Phys. Rev. A, in press

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• Excited states of two-dimensional solitons supported by the spin-orbit coupling and field-induced dipole-dipole repulsion
• Self-trapping under the two-dimensional spin-orbit-coupling and spatially growing repulsive nonlinearity
• Two-dimensional composite solitons in Bose-Einstein condensates with spatially confined spin-orbit coupling
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• Soliton Dimer-soliton scattering in coupled Quasi-one-dimensional Dipolar Bose-Einstein Condensates