Abstract
We report some investigations on the existence of matter-wave solitons when considering cross-combined optical lattices (OL) in three dimensions (3D), where we have a nonlinear OL in one of the directions, which is perpendicular to a two-dimensional (2D) plane with linear OLs in either one or both directions. This study can be useful to manage 3D solitons through spatial modulations of the scattering length in one of the OL directions. Another independent study is reported, by considering bright solitons manifested in a bosonic condensate gas carrying collinear dipole moments, which induces an external polarizing field with strength periodically modulated along one of the coordinates. This leads to an effective nonlocal nonlinear lattice, with solitonic solutions. Their dynamics and mobility can be investigated by an effective one-dimensional (1D) model. Interactions between solitons are also reported within this 1D model. In all the cases, we consider full numerical and variational approaches.
Highlights
In the present contribution we review some recent works on nonlinear optical lattices that we have been investigating in Refs. [1, 2]
In perspective of potential applications, we should point out that, besides providing an alternate way to create stable solitons in 3D, with cross-combined linear and nonlinear optical lattices, these results can be useful in practical applications, opening the possibility to manage stable 3D solitons through spatial modulations of the scattering length in one of the optical lattice directions
In perspective of potential applications, we should point out that, besides providing an alternate way to create stable solitons in 3D, with cross combined linear and nonlinear optical lattices, these results can be useful in practical applications, opening the possibility to manage stable 3D solitons through spatial modulations of the scattering length in one of the OL directions
Summary
In the present contribution we review some recent works on nonlinear optical lattices that we have been investigating in Refs. [1, 2]. Such dipole moments are induced by an external polarizing field with the strength periodically modulated along the coordinate. Is a quasi-1D dipolar Bose-Einstein condensate (BEC) with electric dipole moments of particles induced by the dc field with the local strength periodically varying in space, while its direction is uniform, being oriented along the system’s axis, giving rise to the attractive DDI In both sections the reported results were obtained from exact numerical simulations, as well as from variational procedures, as detailed in [1, 2].
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