Trapped Bose-Einstein Condensates: Role of Dimensionality

TL;DR

This paper investigates how the spatial dimension affects the structure and stability of trapped Bose-Einstein condensates, revealing stability conditions for positive and negative scattering lengths across 1D, 2D, and 3D cases.

Contribution

It systematically analyzes the influence of dimensionality on BEC stability and links nonlinear modes to solitary waves in the nonlinear Schrödinger framework.

Findings

Ground states are stable in all dimensions for positive scattering length.

Negative scattering length ground states are stable in 1D and 2D, unstable in 3D.

Nonlinear modes of BECs correspond to bright and dark solitary waves.

Abstract

We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1,2,3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external anisotropic parabolic potential. While for the positive scattering length the stationary ground-state solutions of the Gross-Pitaevskii equation are shown to be always stable independently of the spatial dimension, for the negative scattering length the ground-state condensate is stable only in the 1D and 2D cases, whereas in the 3D case it becomes unstable. A direct link between nonlinear modes of BECs and (bright and dark) solitary waves of the nonlinear Schrodinger equation is demonstrated for all the dimensions.