Stability of Bose-Einstein Condensates Confined in Traps

TL;DR

This paper reviews the stability of trapped Bose-Einstein condensates, analyzing their static and dynamic properties, including collapse phenomena for attractive interactions, using variational methods and the Gross-Pitaevskii equation.

Contribution

It provides a comprehensive review of recent theoretical studies on the stability and collapse of trapped Bose-Einstein condensates, including two-component systems and nonlinear dynamics.

Findings

Collapse occurs for attractive inter-atomic potentials, setting an upper atom number limit.

Static ground state properties are analyzed via variational methods.

Time evolution described by the nonlinear Schrödinger equation reveals finite-time singularities.

Abstract

Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by use of the variational method. The anlysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross-Pitaevskii equation which is known in nonlinear physics as the nonlinear Schr\"odinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.