Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate

TL;DR

This paper analyzes the stability of three-dimensional breather solitons in Bose-Einstein Condensates with Feshbach resonance management, combining theoretical methods and numerical simulations to identify stable regimes under various confinement conditions.

Contribution

It provides a comprehensive stability analysis of 3D breather solitons in BECs, including the effects of different confinement strengths and a comparison with quasi-2D models, supported by numerical simulations.

Findings

Stability regions split into two parts in 3D analysis.

Tighter confinement shifts stability regions towards higher frequencies.

Numerical simulations confirm theoretical predictions and suggest experimental creation methods.

Abstract

We investigate the stability properties of breather soliton trains in a three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is con ned only by a one dimensional optical lattice and we consider both strong, moderate, and weak con nement. By strong con nement we mean a situation in which a quasi two dimensional soliton is created. Moderate con nement admits a fully three dimensional soliton. Weak con nement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in e ective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully con rmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We nd that in the 3D case the stability region splits into two parts. However, as we tighten the con nement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for quasi 2D. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust 3D solitons in experiments in a Bose Einstein Condensate in a one-dimensional lattice.