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

D. Mihalache·D. Mazilu·F. Lederer·B. A. Malomed·L. -C. Crasovan·Y. V. Kartashov·L. Torner
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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.

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D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, L. -C. Crasovan, Y. V. Kartashov, L. Torner. 2005-07-04. Stable three-dimensional solitons in attractive Bose-Einstein condensates loaded in an optical lattice. https://doi.org/10.1103/physreva.72.021601

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