Matter-wave gap solitons and vortices in three-dimensional parity-time-symmetric optical lattices

Past decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensional PT optical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems

Automated summary

The emergence and expansion of parity-time (PT)-symmetric systems in various physical fields have been observed in the past decades, despite being non-Hermitian, they exhibit completely real spectra. While the exploration of nonlinear waves in low-dimensional PT-symmetric non-Hermitian systems has been extensive, understanding these systems in higher dimensions is still difficult. This study surveys matter-wave nonlinear gap modes of Bose-Einstein condensates in three-dimensional PT optical lattices with repulsive interparticle interactions, focusing on multidimensional gap solitons and vortices. Through theoretical and numerical simulations, stability and instability areas of localized modes within the linear band gap spectra are investigated. The study provides a deep and consistent understanding of the formation, structural property, and dynamics of coherent localized matter waves supported by PT optical lattices in multidimensional space, which opens up possibilities for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.