Abstract. We study three-dimensional vortex lattice structures in purely dipolar Bose-Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio (λ) and dipole-dipole interaction strength (D) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross-Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.
We study stability of solitary vortices in the two-dimensional trapped Bose-Einstein condensate (BEC) with a spatially localized region of self-attraction. Solving the respective Bogoliubov-de Gennes equations and running direct simulations of the underlying Gross-Pitaevskii equation reveals that vortices with topological charge up to S = 6 (at least) are stable above a critical value of the chemical potential (i.e., below a critical number of atoms, which sharply increases with S). The largest nonlinearity-localization radius admitting the stabilization of the higher-order vortices is estimated analytically and accurately identified in a numerical form. To the best of our knowledge, this is the first example of a setting which gives rise to stable higher-order vortices, S > 1, in a trapped self-attractive BEC. The same setting may be realized in nonlinear optics too.
We explore stability regions for solitons in the nonlinear Schrödinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign. This setting can be implemented in optical waveguides based on colloids of nanoparticles. The solitons' stability is identified by solving linearized equations for small perturbations, and is found to fully comply with the Vakhitov-Kolokolov criterion. In the limit case of tight confinement of the nonlinearity, results are obtained in an analytical form, approximating the confinement profile by a delta-function. It is found that the confinement greatly increases the largest total power of stable solitons, in the case when the quintic term is defocusing, which suggests a possibility to create tightly confined high-power light beams guided by the spatial modulation of the local nonlinearity strength.
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