Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice

Abstract

The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of ${}^7$Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is $\approx 6$ recoil energies in the lattice. The respective energy-vs.-norm diagram features two cuspidal points, resulting in a typical \textit{swallowtail pattern}, which is a generic feature of 3D solitons supported by low- (2D) or fully-dimensional lattice potentials.

8 pages, 6 figures, to appear in Physical Review A

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• Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
• Bose-Einstein condensation: Twenty years after
• A model of a dual-core matter-wave soliton laser
• From Feshbach-Resonance Managed Bose-Einstein Condensates to Anisotropic Universes: Some Applications of the Ermakov-Pinney equation with Time-Dependent Nonlinearity
• Analytic theory of narrow lattice solitons
• Structure and stability of two-dimensional Bose-Einstein condensates under both harmonic and lattice confinement
• Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices
• Gap-Townes solitons and delocalizing transitions of multidimensional Bose-Einstein condensates in optical lattices