Fate of a Bose-Einstein condensate with attractive interaction

TL;DR

This paper investigates the decay mechanisms of a Bose-Einstein condensate with attractive interactions, revealing a critical particle number that determines whether decay occurs via quantum tunneling or collapse into a dense 'black hole' state.

Contribution

It introduces a novel analysis of condensate decay using Feynman path integrals and identifies a critical particle number for different decay regimes.

Findings

Condensate decays slowly below critical particle number

Collapse occurs above critical particle number with large density fluctuations

Quantum tunneling acts as a hydrodynamic source feeding the black hole

Abstract

We calculate the decay amplitude of a harmonically trapped Bose-Einstein condensate with attractive interaction via the Feynman path integral. We find that when the number of particles is less than a critical number, the condensate decays relatively slowly through quantum tunneling. When the number exceeds the critical one, a "black hole" opens up at the center of the trap, in which density fluctuations become large due to a negative pressure, and collisional loss will drain the particles from the trap. As the black hole is fed by tunneling particles, we have a novel system in which quantum tunneling serves as a hydrodynamic source.