Matter-wave solitons with the minimum number of particles in two-dimensional quasiperiodic potentials

TL;DR

This study investigates 2D matter-wave solitons in quasiperiodic potentials, focusing on their stability, minimal particle number, and dynamical properties, using numerical methods based on the Gross-Pitaevskii equation.

Contribution

It provides a systematic numerical analysis of 2D soliton families near stability thresholds in quasiperiodic potentials, highlighting stability criteria and instability mechanisms.

Findings

Single-peak solitons follow the VK stability criterion.

Double-peak solitons are inherently unstable against splitting.

Minimum particle number facilitates soliton creation near stability thresholds.

Abstract

We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution attains a minimum, facilitating the creation of the soliton. The model is based on the Gross-Pitaevskii equation for the self-attractive condensate loaded into a quasiperiodic (QP) optical lattice (OL). The same model applies to spatial optical solitons in QP photonic crystals. Dynamical properties and stability of the solitons are analyzed with respect to variations of the depth and wavenumber of the OL. In particular, it is found that the single-peak solitons are stable or not in exact accordance with the Vakhitov-Kolokolov (VK) criterion, while double-peak solitons, which are found if the OL wavenumber is small enough, are always unstable against splitting.