Gap solitons in Bose–Einstein condensate loaded in a honeycomb optical lattice: Nonlinear dynamical stability, tunneling, and self-trapping

• Published in: Physica A 2021-09, Vol.577, p.126087, Article 126087
• Main Authors: Meng, Hongjuan, Zhou, Yushan, Li, Xiaolin, Ren, Xueping, Wan, Xiaohuan, Zhou, Zhikun, Wang, Wenyuan, Shi, Yuren
• Format: Article
• Language: English
• Subjects: Bose–Einstein condensate; Gap soliton; Honeycomb optical lattices
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2021.126087

We investigate the gap solitons of Bose–Einstein condensate in honeycomb optical lattices. It is found that the two-dimensional honeycomb optical lattices admit multipole gap solitons. These multipoles can have their bright solitary structures be in-phase or out-of-phase. The nonlinear dynamical stabilities of these solitons are investigated using direct simulations of the Gross–Pitaevskii equation. For the unipole gap solitons, the nonlinear evolution shows dynamical stability or instability, which depends on the properties of atomic interactions and the dependence of soliton power. A fascinating property of dipole gap solitons is that they can present self-trapping or tunneling instabilities under atomic nonlinearity. The in-phase and out-of-phase of multipole gap solitons support different tunneling or self-trapping regimes. These results have an application to investigations of localized structures in nonlinear optics and Bose–Einstein condensate. •Varies multipole gap solitons with in-phase or out-of-phase are found.•The nonlinear dynamic stability conditions of the unipole gap solitons are obtained.•The dipole gap solitons are all unstable, their nonlinear dynamic evolution exhibits self-trapping and tunneling instabilities.