Two-dimensional dipolar gap solitons in free space with spin-orbit coupling

Abstract

We present gap solitons (GSs) that can be created in free nearly two-dimensional (2D) space in dipolar spinor Bose-Einstein condensates with the spin-orbit coupling (SOC), subject to tight confinement, with size $a_{\perp }$, in the third direction. For quasi-2D patterns, with lateral sizes $l\gg a_{\perp }$, the kinetic-energy terms in the respective spinor Gross-Pitaevskii equations may be neglected in comparison with SOC. This gives rise to a bandgap in the system's spectrum, in the presence of the Zeeman splitting between the spinor components. While the present system with contact interactions does not produce 2D solitons, stable gap solitons(GSs), with vorticities $0$ and $1$ in the two components, are found, in quasi-analytical and numerical forms, under the action of dipole-dipole interaction (DDI). Namely, isotropic and anisotropic 2D GSs are obtained when the dipoles are polarized, respectively, perpendicular or parallel to the 2D plane. The GS families extend, as \textit{embedded solitons} (ESs), into spectral bands, a part of the ES branch being stable for isotropic solitons. The GSs remain stable if the competing contact interaction, with the sign opposite to that of the DDI, is included, while the addition of the contact term with the same sign destabilizes the GSs, at first replacing them by breathers, and eventually leading to destruction of the solitons. Mobility and collision of the GSs are studied too, revealing negative and positive effective masses of the isotropic and anisotropic solitons, respectively.

13 pages, 8 figures, 54 references, Physical Review A in press

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• Long-living Bloch oscillations of matter waves in optical lattices
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• Modulational instability of matter waves under strong nonlinearity management
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Cited by in corpus (8)

• Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
• Anisotropic semi-vortices in dipolar spinor condensates controlled by Zeeman splitting
• Flipping-shuttle oscillations of bright one- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with Rabi mixing
• Quasi-one-dimensional spin-orbit- and Rabi-coupled bright dipolar Bose-Einstein-condensate solitons
• Tail-free self-accelerating solitons and vortices
• Dipolar bright solitons and solitary vortices in a radial lattice
• Cross-symmetry breaking of two-component discrete dipolar matter-wave solitons
• Gap and embedded solitons in microwave-coupled binary condensates