Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

TL;DR

This paper analyzes the conditions under which Bose-Einstein condensates with long-range attractive interactions of the form 1/r^b can undergo collapse or form stable self-trapped states, revealing critical and supercritical regimes.

Contribution

It provides an exact analysis of collapse conditions and stability for BECs with 1/r^b interactions, identifying critical thresholds and regimes.

Findings

Collapse occurs only for b ≥ 2.

Critical collapse at b=2 requires a minimum number of particles.

Stable self-trapping exists for b<2 without external traps.

Abstract

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential.