Lossy Quantum Defect Theory of Ultracold Molecular Collisions

TL;DR

This paper develops a statistical model for ultracold molecular collisions that accounts for finite complex lifetimes, revealing conditions for universal loss rates and the impact of overlapping resonances on nonuniversal behavior.

Contribution

It introduces a lossy quantum defect theory that explicitly models the finite lifetime of collision complexes and analyzes the effects of overlapping resonances on loss rates.

Findings

Loss cross section equals elastic cross section under certain conditions.

Overlapping resonances lead to Ericson fluctuations and nonuniversal boundary conditions.

Deviations from theory suggest non-chaotic collision dynamics.

Abstract

We consider losses in collisions of ultracold molecules described by a simple statistical short-range model that explicitly accounts for the limited lifetime of classically chaotic collision complexes. This confirms that thermally sampling many isolated resonances leads to a loss cross section equal to the elastic cross section derived by Mayle et al. [Phys. Rev. A 85, 062712 (2012)], and this makes precise the conditions under which this is the case. Surprisingly, we find that the loss is nonuniversal. We also consider the case that loss broadens the short-range resonances to the point that they become overlapping. The overlapping resonances can be treated statistically even if the resonances are sparse compared to $k_BT$, which may be the case for many molecules. The overlap results in Ericson fluctuations which yield a nonuniversal short-range boundary condition that is independent of energy over a range much wider than is sampled thermally. Deviations of experimental loss rates from the present theory beyond statistical fluctuations and the dependence on a background phase shift are interpreted as non-chaotic dynamics of short-range collision complexes.