Dilute Bose-Einstein Condensate in a Trap: Characteristic Lengths and Critical Velocities

TL;DR

This paper investigates how repulsive interactions influence the properties of a dilute Bose-Einstein condensate in a trap, focusing on characteristic lengths and critical velocities using the Bogoliubov approximation and Gross-Pitaevskii equation.

Contribution

It provides a detailed analysis of the effects of interactions on condensate size, speed of sound, and vortex creation thresholds in trapped Bose gases.

Findings

Interactions expand the condensate size compared to ideal gas

Speed of sound depends on the coherence length

Critical angular velocity for vortex creation is influenced by interparticle repulsion

Abstract

The Bogoliubov approximation and the Gross-Pitaevskii equation characterize the effect of repulsive interactions on a dilute ideal Bose-Einstein gas in a spherical harmonic trap. For large $N$, the interactions expand the condensate relative to an ideal Bose gas; both the speed of sound and critical angular velocity $\Omega_{c1}$ for creation of a quantized vortex depend crucially on the interparticle repulsion through the coherence length $\xi$.