Scaling laws governing the collapse of a Bose-Einstein condensate

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 Schrödinger equation. We find good agreement between our simulations and the atom-loss measurements with a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi mathvariant="normal">K</a:mi><a:mprescripts/><a:none/><a:mn>39</a:mn></a:mmultiscripts></a:math> condensate. Our simulations reveal an interplay of weak collapse and the propensity of the system to form a hotspot and we uncover scaling laws that govern this behavior. We also identify promising signatures of the theoretically predicted, but so far experimentally elusive, elastic three-body interactions.