Scaling Laws Governing the Collapse of a Bose-Einstein Condensate

TL;DR

This paper investigates the collapse dynamics of an attractive Bose-Einstein condensate using numerical simulations, revealing new scaling laws, the formation of hotspots, and signatures of elusive three-body interactions, aligning well with experimental data.

Contribution

It introduces novel scaling laws for condensate collapse and identifies signatures of three-body interactions through detailed numerical analysis.

Findings

Good agreement with atom-loss measurements

Discovery of new collapse scaling laws

Identification of signatures of three-body interactions

Abstract

We study the collapse of an attractive Bose-Einstein condensate, where an unstable system evolves towards a singularity, by numerically solving the underlying cubic-quintic nonlinear Schr\"odinger equation. We find good agreement between our simulations and the atom-loss measurements with a $^{39}$K condensate. Our simulations reveal an interplay of weak collapse and the propensity of the system to form a hotspot, and we uncover new scaling laws that govern this behavior. We also identify promising signatures of the theoretically predicted, but so far experimentally elusive, elastic three-body interactions.