Lossy quantum defect theory of ultracold molecular collisions

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 B T , 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 nonchaotic dynamics of short-range collision complexes.

Anomalous Lifetimes of Ultracold Complexes Decaying into a Single Channel: What's Taking So Long in There?

“…Thus in a gas of temperature T ≈ 0.5 µK, the number of resonances directly relevant would be of order unity at best, and far below this in general. Additional resonances could be relevant if they are very broad, but this remains uncertain at present [40].…”

Quantum control of reactions and collisions at ultralow temperatures

“…The RRKM model may be applicable. 130 For atom–molecule collisions, the density of states is much lower and the mean spacing between neighboring states is much larger than the temperature of the molecular gases. In this case, thermal averaging may be inappropriate.…”

Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms

“…In the absence of other loss processes, this implies a mean lifetime τ = 2π ρ/T inc , but only if the thermal energy spread is large compared to Γinc as described above. Christianen et al [83] recently considered a lossy QDT model of such resonances. They concluded that if the complexes are lost rapidly once formed and Γs inc = d/2π, such that T s inc = 1 in equation ( 3), the loss rate is represented by y = 0.25, as opposed to the y = 1 implicit in the model of Croft et al [82].…”

“…However, when many resonances overlap, they reach the regime of Ericson fluctuations [80] and the total loss cannot be represented in this way. This situation has been considered by Christianen et al [83]. Here we will consider only the case Γ inel < d, which is applicable to typical alkali atom + diatom collisions.…”