Abstract
We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two- and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form. We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers (or norm of the spinor wavefunction) exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point. The zero-threshold point is a boundary between single-peaked and striped states, realizing hybrids combining 2D and 1D structural features. In a vicinity of such point, an asymptotic equation describing the bifurcation of the solitons from the linear spectrum is derived and investigated analytically. We show that striped 3D solitary states are as well stabilized by 2D SOC, albeit in a limited range of chemical potentials and norms.
Highlights
AND MODELUnlike one-dimensional (1D) settings, where stable soliton states exist in diverse systems, stability is a major issue for multidimensional self-trapped localized states [1,2]
We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two- and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form
We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point
Summary
Unlike one-dimensional (1D) settings, where stable soliton states exist in diverse systems, stability is a major issue for multidimensional self-trapped localized states [1,2]. While LHY-stabilized 3D [18] and 2D [19,20] vortical droplets have been predicted in BECs with contact nonlinearity Another possibility for the creation of stable solitons in atomic BECs was predicted in the model of spinor condensates with a cubic attraction and spin-orbit coupling (SOC) between the two components [21,22,23] We explore the possibility to create stable 2D and 3D self-trapped states supported by lower-dimensional SOC (1D and 2D, respectively). Such settings suggest the existence of a different species of multidimensional solitons, which strongly differ from the solitons supported by the full SOC. Their stability is a challenging issue, as the reduction of the dimensionality of the support structure makes
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