Three-Dimensional Solitary Waves and Vortices in a Discrete Nonlinear Schr{ö}dinger Lattice

Abstract

In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schr{ö}dinger equation, we find discrete vortex solitons with various values of the topological charge $S$. Stability regions for the vortices with $S=0,1,3$ are investigated. The S=2 vortex is unstable, spontaneously rearranging into a stable one with S=3. In a two-component extension of the model, we find a novel class of stable structures, consisting of vortices in the different components, perpendicularly oriented to each other. Self-localized states of the proposed types can be observed experimentally in Bose-Einstein condensates trapped in optical lattices, and in photonic crystals built of microresonators.

4 pages, 5 figures. To appear in Phys. Rev. Lett. (2004)

References in corpus (3)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Multidimensional solitons in periodic potentials
• Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability

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