We describe the band-gap spectrum and localized coherent-matter waves in twodimensional optical lattices, and predict the existence of novel types of soliton bound states with a vortex-like phase, the gap vortices.
We study the localization of vortices in a three-dimensional band-gap. We report that not only planar, two-dimensional matter-wave gap vortices persist in the presence of the third dimension, but also the three-dimensional lattice may support novel types of quite unusual vortex-like structures which survive perturbations of both phase and atomic density. One remarkable result of the lattice geometry is that we may study coherent interactions of planar vortices, and even find stationary structures of an arbitrarily long stack of vortices. We find that the lattice stabilizes the vortex line, and leads to robust evolution of the perturbed state. The three-dimensional geometry also allows the existence of exotic vortex states which have no two-dimensional equivalent
We overview our recent theoretical studies on nonlinear atom optics of the Bose-Einstein condensates (BECs) loaded into optical lattices. In particular, we describe the band-gap spectrum and nonlinear localization of BECs in one- and two-dimensional optical lattices. We discuss the structure and stability properties of spatially localized states (matter-wave solitons) in 1D lattices, as well as trivial and vortex-like bound states of 2D gap solitons. To highlight similarities between the behavior of coherent light and matter waves in periodic potentials, we draw useful parallels with the physics of coherent light waves in nonlinear photonic crystals and optically-induced photonic lattices.
Past decades have witnessed the emergence and increasing expansion of parity-time (PT )-symmetric systems in diverse physical fields and beyond as they license entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensional PT -symmetric non-Hermitian systems have recently been explored broadly, whose understanding 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. Relying on direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linearband 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, opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systems.