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arXiv:1812.10218 · Physics Letters A

Soliton lattices in the Gross–Pitaevskii equation with nonlocal and repulsive coupling

Hidetsugu Sakaguchi

Published Jan 8, 2019• 1 citation
arXivHTMLPDF
DOI
10.1016/j.physleta.2018.12.036

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The Gross–Pitaevskii equation for two-component rotating Bose–Einstein condensates with the Rashba-type spin–orbit (SO) coupling is studied with numerical simulations and variational analyses. A multiquantum vortex state becomes a ground state in a harmonic potential when mutual interaction is absent. When the attractive interaction is strong, the multiquantum vortex state exhibits modulational instability in the azimuthal direction, and a soliton-like state appears. When the repulsive interaction is strong, a vortex lattice state with a multiquantum vortex at the center is created. We find that the vortex lattice state is approximated at a linear combination of multiquantum vortex states.
We show that the dark soliton of the Gross-Pitaevskii equation (GPE) that describes the Bose-Einstein condensate (BEC) density of a system of weakly repulsive bosons, also describes that of a system of strongly repulsive hard core bosons at half filling. This connection establishes a relationship between the GPE soliton and the magnetic soliton of an easy-plane ferromagnet, where the BEC density relates to the square of the in-plane magnetization of the system. This mapping between well known solitons in two distinct physical systems provides an intuitive understanding of various characteristics of the solitons.
In this paper, we investigate the nonlocal Gross–Pitaevskii equation which describes the phenomena of Bose–Einstein condensates under the mean field approximation. Using mean-field theory and adopting separation of variables method, the five-component Gross–Pitaevskii spin–orbit-coupled spin-2 Bose–Einstein condensate model can be reduced to five-component ordinary differential equation, then twelve families of solutions are obtained by the combination of some Jacobi elliptic functions. In particular, when the modulus of Jacobi elliptic function tends to one, a series of bright soliton and dark soliton and their combined solution are obtained. These periodic and hyperbolic soliton solutions are analyzed in detail, the nature and images will be of practical application to provide theoretical guidance for spin systems.