A Statistical Theory for Lifetimes of Ultracold Collision Complexes

A significant challenge in the pursuit of better ultracold molecules is the large two body loss experienced by these systems. When molecules collide at short range, they form long-lived four body collision complexes that are easily lost from the trap, contributing to large two body losses. The conventional Rice–Ramsperger–Kassel–Marcus (RRKM) theory postulates that the long lifetimes of the complexes are proportional to the large density of states arising from many ro-vibrational modes, but experimentally observed lifetimes have shown discrepancies of up to 5 order of magnitude from theoretical predictions. In this work, we investigate the lifetimes of collision complexes starting from a statistical model of resonances using random matrix theory. We numerically sample Hamiltonians from the Gaussian orthogonal ensemble and utilize results from quantum defect theory to calculate scattering properties and lifetimes for the ensemble. We find that in the limit of dense resonances, our theory agrees well with the RRKM prediction, whereas in the limit of sparse resonances, the statistical picture does not well capture the physics of real systems. Finally, we propose a few explanations for the anomalously long lifetimes observed in experiments.