Abstract
Solitons are self-trapped modes existing in various nonlinear systems. Creating stable solitons in two- and three-dimensional settings is a challenging goal in various branches of physics. Several methods have been developed theoretically and experimentally to achieve this, but few of them can support stable multi-dimensional solitons in free space. Recently, a new scheme using spin-orbit-coupling (SOC) has been proposed to create stable 2D solitons in Bose–Einstein condensates (BECs). This paper reviews recent theoretical progress on creating stable 2D solitons in spinor dipolar BEC with SOC, combined with long-range dipole-dipole interaction (DDI), Zeeman splitting (ZS) and contact nonlinearity, in free space. The continuous family of stable symmetric vortex solitons (SVS), asymmetric vortex solitons (AVS), as well as gap solitons (GS) is found via different settings. Their existence and stability conditions are summarized and discussed in detail. The mobility properties of these types of solitons are also addressed. For SVS, a potential method to manipulate its shape and mobility is investigated. These results are supposed to enrich our understanding of 2D solitons and help create multi-dimensional solitons in experiments.
Highlights
Creating stable solitons or self-trapped modes in systems with a dimension higher than one remains a challenging and attractive problem in physics, both in theory and experiments [1,2]
We discussed in this review several settings of creating stable vortex 2D solitons in free space
By SOC combined with attractive anisotropic dipole-dipole interaction (DDI), the continuous family of symmetric (SVS) and asymmetric (AVS) vortex soliton can be produced in spinor Bose–Einstein condensates (BECs)
Summary
Creating stable solitons or self-trapped modes in systems with a dimension higher than one remains a challenging and attractive problem in physics, both in theory and experiments [1,2]. Settings of SOC dipolar BEC combined with cubic contact interactions are considered [60], and stable isotropic and anisotropic gap solitons are found and their properties and stable conditions analyzed, as well as the mobility of these solitons. These results will help to investigate 2D stable vortices in an SOC BEC system experimentally in the future and provide potential manipulation methods [58,59,60].
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