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arXiv:physics/0304052 · Physical Review Letters

Three-Body Recombination at Large Scattering Lengths in an Ultracold Atomic Gas

Tino Weber, Jens Herbig, Michael F. Mark, Hanns‐Christoph Nägerl, Rudolf Grimm

Published Sep 18, 2003• 279 citations
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Abstract

We study three-body recombination in an optically trapped ultracold gas of cesium atoms with precise magnetic control of the s-wave scattering length a. At large positive values of a, we measure the dependence of the rate coefficient on a and confirm the theoretically predicted scaling proportional to a(4). Evidence of recombination heating indicates the formation of very weakly bound molecules in the last bound energy level.

DOI
10.1103/physrevlett.91.123201

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We study three-body recombination in an optically trapped ultracold gas of cesium atoms with precise magnetic control of the s-wave scattering length a. At large positive values of a, we measure the dependence of the rate coefficient on a and confirm the theoretically predicted scaling proportional to a(4). Evidence of recombination heating indicates the formation of very weakly bound molecules in the last bound energy level.
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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.
We combine theory and experiment to investigate five-body recombination in an ultracold gas of atomic cesium at negative scattering length. A refined theoretical model, in combination with extensive laboratory tunability of the interatomic interactions, enables the five-body resonant recombination rate to be calculated and measured. The position of the new observed recombination feature agrees with a recent theoretical prediction and supports the prediction of a family of universal cluster states at negative a that are tied to an Efimov trimer.
Using the knowledge of two-body collision properties that has recently become available, we estimate the three-body recombination rate for doubly-spin-polarized ultracold gas samples of 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb on the basis of the Jastrow approximation. We find that only recombination leading to the formation of the highest two-body bound states is important. The rate for the highest bound level with zero angular momentum is found to increase strongly with the absolute value of the two-body scattering length. \textcopyright{} 1996 The American Physical Society.
An effective field theory for the three-body system with large scattering length is applied to three-body recombination to a weakly bound s-wave state in a Bose gas. Our model independent analysis demonstrates that the three-body recombination constant alpha is not universal, but can take any value between zero and 67.9Planck's over 2pia(4)/m, where a is the scattering length. Other low-energy three-body observables can be predicted in terms of a and alpha. Near a Feshbach resonance, alpha should oscillate between those limits as the magnetic field B approaches the point where a-->infinity. In any interval of B over which a increases by a factor of 22.7, alpha should have a zero.