Universality constraints on three-body recombination for cold atoms: FromHe4toCs133

Abstract

For atoms with large scattering length, the dependence of the 3-body recombination rate on the collision energy is determined by the scattering length and the Efimov 3-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the 3-body recombination rate for 4 He atoms to constrain the universal functions. We then use those universal functions to calculate the 3-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the 4 He results are strong if the scattering length is near the minimum of the 3-body recombination rate at threshold. We apply our results to 133 Cs atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.

Scaling functions applied to three-body recombination ofCs133atoms

“…Starting with S-matrix element for 3-atom to dimer-atom scattering, it was shown in [11] that under the assumption s 11 = 0 the recombination rate can be written as…”

“…[11], the effects of deep dimers can easily be incorporated through one additional parameter η * by making the substitution ln a * 0 → ln a * 0 − iη * /s 0 (11) in, e.g. Eq.…”

“…Here, we relax all but one of the simplifying assumptions made in [11] and extract a set of three independent universal functions capable of parameterizing the three-body recombination rate over a wide range of energies. We test the performance of these universal functions using "data" generated from phase shift calculations [13] …”

“…However, a striking way to demonstrate universality is to describe observables of one system with information which has been extracted from a completely different system. In [11], the authors considered Efimov's radial laws which parameterize the three-atom S-matrix in terms of six real universal functions which depend only on a dimensionless scaling variable, x = (ma 2 E/h 2 ) 1/2 , and phase factors which only contain the three-body parameter. In this work, simplifying assumptions justified over a restricted range of x were made to reduce the six universal functions required to parameterize the three-body recombination rate to just a single function.…”

“…It follows that |s 11 (0)| ≃ 0.002. The first simplifying assumptions being made in [11] was that this function remains small (i.e. ; ≪ 1) for all x and can be ignored.…”