Collapse of a Bose Condensate with Attractive Interactions

TL;DR

This paper investigates the decay of metastable Bose-Einstein condensates with attractive interactions using the Gross-Pitaevskii model, applying instanton formalism and collective coordinate methods to analyze collapse dynamics.

Contribution

It introduces a combined approach using instanton formalism and collective coordinates to study condensate decay, extending previous models with numerical solutions and improved agreement.

Findings

Good agreement between instanton and collective coordinate methods

Numerical solutions of the instanton configuration

Effective mass adjustment improves model accuracy

Abstract

We examine the Gross-Pitaevskii (GP) model for Bose-Einstein condensates in parabolic traps with attractive interactions. The decay of metastable condensates is investigated by applying the instanton formalism to the GP field theory. Employing various dynamical trial states, we derive within a coherent state path integral approach a collective coordinate description in terms of the condensate radius, in agreement with (and extending) earlier results. We then solve numerically for the complete instanton field configuration and compare with the collective coordinate approach. Adjusting only the effective mass of the collective coordinate, the two schemes are then in good agreement.