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arXiv:nlin/0612055 · Physical Review A

Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates

Volodymyr M. Lashkin

Published Apr 11, 2007• 68 citations
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Abstract

We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.

DOI
10.1103/physreva.75.043607

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We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.
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We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.
By solving the two-dimensional, nonlocal Gross-Pitaevskii equation numerically, we study the hydrodynamics of quantized vortices in a dipolar Bose-Einstein condensate excited by an oscillating potential. We calculate the critical velocity for the vortex nucleation in the presence and absence of dipole-dipole interaction. Above a critical velocity, the oscillating potential nucleates the vortex pairs, whose impulses alternatively change their direction synchronously with the oscillation of the Gaussian potential. We study the dynamics of the vortices and also the formation of the dark solitons which have not been previously reported in a dipolar Bose-Einstein condensate.
We study formation of rotating three-dimensional high-order solitons (azimuthons) in Bose Einstein condensate with attractive nonlocal nonlinear interaction. In particular, we demonstrate formation of toroidal rotating solitons and investigate their stability. We show that variational methods allow a very good approximation of such solutions and predict accurately the soliton rotation frequency. We also find that these rotating localized structures are very robust and persist even if the initial condensate conditions are rather far from the exact soliton solutions. Furthermore, the presence of repulsive contact interaction does not prevent the existence of those solutions, but allows one to control their rotation. We conjecture that self-trapped azimuthons are generic for condensates with attractive nonlocal interaction.