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Physical Review Letters

Recombination of Three Atoms in the Ultracold Limit

Brett D. Esry, Chris H. Greene, James P. Burke

Published Aug 30, 1999• 441 citations
Publisher

Abstract

We identify two qualitatively different mechanisms that control three-body recombination in a spin-polarized gas near zero temperature. A universal curve describes the recombination rate versus the two-body scattering length $a$. It grows as ${a}^{4}$ for large $|a|,$ with different mechanisms for $a<0$ and $a>0$. Our calculations document a previously established mechanism that causes ${K}_{3}$ to grow rapidly as the two-body scattering length $a$ increases toward $+\ensuremath{\infty}$, and a new tunneling mechanism that produces an even stronger enhancement of ${K}_{3}$ as $a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The expectations based on these two mechanisms can be modified by quantum mechanical interference or resonance effects.

DOI
10.1103/physrevlett.83.1751

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We identify two qualitatively different mechanisms that control three-body recombination in a spin-polarized gas near zero temperature. A universal curve describes the recombination rate versus the two-body scattering length aaa. It grows as a4{a}^{4}a4 for large ∣a∣,|a|,∣a∣, with different mechanisms for a<0a<0a<0 and a>0a>0a>0. Our calculations document a previously established mechanism that causes K3{K}_{3}K3​ to grow rapidly as the two-body scattering length aaa increases toward +\ensuremath∞+\ensuremath{\infty}+\ensuremath∞, and a new tunneling mechanism that produces an even stronger enhancement of K3{K}_{3}K3​ as a\ensuremath→\ensuremath−\ensuremath∞a\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}a\ensuremath→\ensuremath−\ensuremath∞. The expectations based on these two mechanisms can be modified by quantum mechanical interference or resonance effects.
Three-body recombination of identical, spin-polarized fermionic atoms in the ultracold limit is investigated using model interactions. The mechanisms for recombination are parametrized by the "scattering volume" V(p) and described in the framework of the adiabatic hyperspherical representation. We have calculated the recombination rate K3 as a function of V(p) and have found K3 proportional, variant |V(p)|(8/3) for small |V(p)|. Recombination near a two-body Feshbach resonance can thus be significant.
Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length aaa of the He-He interaction and a three-body parameter a∗{a}_{*}a∗​ as input, where a∗{a}_{*}a∗​ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to 1/a∗1/{a}_{*}1/a∗​ versus 1/a1/a1/a should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational 1/a∗1/{a}_{*}1/a∗​ versus 1/a1/a1/a to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum J>0J>0J>0 are also discussed.
We discuss three-body recombination of ultracold atoms to a weakly bound sss level. In this case, characterized by large and positive scattering length aaa for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: ${\ensuremath{\alpha}}_{\mathrm{rec}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3.9\ensuremath{\Elzxh}{a}^{4}/m$, where mmm is the atom mass.
Recombination of identical, spin-polarized fermions in cold three-body collisions is investigated. We parametrize the mechanisms for recombination in terms of the `scattering volume' V p and another length scale r 0 . Model two-body interactions were used within the framework of the adiabatic hyperspherical representation. We examine the recombination rate K 3 as a function of the collision energy E for various values of V p . Not only do we consider the dominant J Π = 1 + case, but also the next-leading order contributions from J Π = 1 - and 3 - . We discuss the behaviour near a two-body resonance and the expected universality of fermionic recombination. Comparisons with boson recombination are considered in detail.
For identical bosons with a large scattering length, the dependence of the three-body recombination rate on the collision energy is determined in the zero-range limit by universal functions of a single scaling variable. There are six scaling functions for angular momentum zero and one scaling function for each higher partial wave. We calculate these universal functions by solving the Skorniakov-Ter-Martirosian equation. The results for the three-body recombination as a function of the collision energy are in good agreement with previous results from solving the three-body Schr\"odinger equation for 4He^{4}\mathrm{He}4He atoms. The universal scaling functions can be used to calculate the three-body recombination rate at nonzero temperature. We obtain an excellent fit to the data from Grimm and co-workers for 133Cs^{133}\mathrm{Cs}133Cs atoms with a large positive scattering length.
For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for 4He^{4}\mathrm{He}4He atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the 4He^{4}\mathrm{He}4He results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to 133Cs^{133}\mathrm{Cs}133Cs atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.