Delocalizing transition of multidimensional solitons in Bose-Einstein condensates

TL;DR

This paper investigates the critical delocalization transition of multidimensional solitons in Bose-Einstein condensates within optical lattices, revealing dimension-dependent behaviors and proposing a quantum bound state interpretation.

Contribution

It provides a detailed analysis of the delocalizing transition in 2D and 3D optical lattices and introduces a quantum bound state perspective.

Findings

Bright solitons in 2D and 3D OLs undergo abrupt delocalization below critical OL strength.

In 1D OLs, bright solitons remain stable across parameter variations.

The delocalization is interpreted through quantum bound state theory.

Abstract

Critical behavior of solitonic waveforms of Bose-Einstein condensates in optical lattices (OL) has been studied in the framework of continuous mean-field equation. In 2D and 3D OLs bright matter-wave solitons undergo abrupt delocalization as the strength of the OL is decreased below some critical value. Similar delocalizing transition happens when the coefficient of nonlinearity crosses the critical value. Contrarily, bright solitons in 1D OLs retain their integrity over the whole range of parameter variations. The interpretation of the phenomenon in terms of quantum bound states in the effective potential is proposed.