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arXiv:cond-mat/0206317 · Physical Review A

Weakly bound atomic trimers in ultracold traps

Marcelo Takeshi Yamashita, T. Frederico, Lauro Tomio, A. Delfino

Published Sep 15, 2003• 14 citations
arXivHTMLPDF

Abstract

The experimental three-atom recombination coefficients of the atomic states ${}^{23}\mathrm{Na}|{F=1,m}_{F}=\ensuremath{-}1〉,$ ${}^{87}\mathrm{Rb}|{F=1,m}_{F}=\ensuremath{-}1〉,$ and ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ together with the corresponding two-body scattering lengths, allow predictions of the trimer bound-state energies for such systems in a trap. The recombination parameter is given as a function of the weakly bound trimer energies, which are in the interval $1<m(a/\ensuremath{\Elzxh}{)}^{2}{E}_{3}<6.9$ for large positive scattering lengths $a.$ The contribution of a deep-bound state to our prediction, in the case of ${}^{85}\mathrm{Rb}|{F=2,m}_{F}=\ensuremath{-}2〉,$ for a particular trap, is shown to be relatively small.

DOI
10.1103/physreva.68.033406

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We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.
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.
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