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Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction

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  • Chen, Zhiming
  • Liu, Xiuye
  • Xie, Hongqiang
  • Zeng, Jianhua

Abstract

Compared with low-dimensional solitons that are widely studied in various realizable nonlinear physical systems, the properties and dynamics of three-dimensional solitons and vortices have not been well disclosed yet. Using numerical simulations and theoretical analysis, we here address the existence, structural property, and dynamics of three-dimensional gap solitons and vortices (with topological charge s=1) of Bose–Einstein condensates moving by Lévy flights (characterized by fractional diffraction operators, Lévy index 1<α≤2) in optical lattices. We stress that previously the localized modes have only been revealed in low-dimensional nonlinear fractional systems in one- and two-dimensional periodic potentials, our study presented here thus drives the associated nonlinear-wave research into three-dimensional configurations. The three-dimensional optical lattices exhibit a nontrivial wide band-gap feature, within which the matter-wave localized gap modes could be excited. The stability and instability regions of both three-dimensional gap modes are obtained via direct perturbed simulations, shedding light on multidimensional soliton physics in nonlinear fractional systems with periodic potentials.

Suggested Citation

  • Chen, Zhiming & Liu, Xiuye & Xie, Hongqiang & Zeng, Jianhua, 2024. "Three-dimensional Bose–Einstein gap solitons in optical lattices with fractional diffraction," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001097
    DOI: 10.1016/j.chaos.2024.114558
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    References listed on IDEAS

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    1. Chen, Zhiming & Wu, Zexing & Zeng, Jianhua, 2023. "Light gap bullets in defocusing media with optical lattices," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Bao, Y.Y. & Li, S.R. & Liu, Y.H. & Xu, T.F., 2022. "Gap solitons and nonlinear Bloch waves in fractional quantum coupler with periodic potential," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Malomed, B.A., 2022. "Multidimensional dissipative solitons and solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Shilong Liu & Yingwen Zhang & Boris A. Malomed & Ebrahim Karimi, 2023. "Experimental realisations of the fractional Schrödinger equation in the temporal domain," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    5. Chen, Junbo & Zeng, Jianhua, 2021. "Dark matter-wave gap solitons of Bose-Einstein condensates trapped in optical lattices with competing cubic-quintic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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