Gap-Townes solitons and delocalizing transitions of multidimensional Bose-Einstein condensates in optical lattices

TL;DR

This paper demonstrates the existence of gap-Townes solitons in multidimensional Bose-Einstein condensates within optical lattices, revealing a transition between stable localized states and decay, and linking these to higher-order nonlinear Schrödinger solutions.

Contribution

It introduces the concept of gap-Townes solitons in multidimensional BECs with optical lattices, highlighting their stability properties and the delocalizing transition.

Findings

Existence of gap-Townes solitons in 2D and 3D optical lattices.

Identification of a delocalizing transition separating stable and unstable solutions.

Connection between multidimensional solutions and higher-order nonlinear Schrödinger equations.

Abstract

We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in two- and three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schr\"odinger equation, sharing with these the propriety of being unstable against small norm (number of atoms) variations. We show that in the presence of the optical lattice the solution separates stable localized solutions (gap-solitons) from decaying ones, characterizing the delocalizing transition occurring in the multidimensional case. The link between these higher dimensional solutions and the ones of one dimensional nonlinear Schr\"odinger equation with higher order nonlinearities is also discussed.