Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

TL;DR

This paper demonstrates the existence and stabilization of multidimensional matter-wave solitons in a crossed linear and nonlinear optical lattice setup, combining analytical and numerical methods to confirm their stability.

Contribution

It introduces a novel crossed optical lattice configuration that stabilizes 2D matter-wave solitons against decay or collapse for both attractive and repulsive interactions.

Findings

Stable 2D solitons are achieved in the crossed OL setup.

Analytical variational and numerical methods agree on soliton stability.

Crossed linear and nonlinear OLs enable control over soliton dynamics.

Abstract

It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance. In particular, we show that such crossed linear and nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good agreement of the results corresponding to both treatments is observed.