Abstract
The problem of three interacting quantal bodies, in its various guises, seems deceptively simple, but it has also provided striking surprises, such as the Efimov effect1,2, which was confirmed experimentally3 only more than 35 years after its initial prediction. The importance of understanding the three-body problem was magnified by the explosion of ultracold science following the formation of Bose–Einstein condensates in 1995 (ref. 4). For ultracold gases, three-body recombination (where B+B+B collide to form B2+B) was quickly recognized as the main loss process and connected5,6,7,8 with the Efimov effect in the ‘universal’ realm of very large atom–atom scattering lengths a. The problem of four interacting bodies challenges theory far more than the three-body quantal problem. Some key insights have been achieved in recent years9,10,11,12,13,14,15,16. Here, we present a major extension of our understanding of the four-body problem in the universal large-a regime. Our results support a previous conjecture10 that two resonantly bound four-body states are attached to every universal three-body Efimov resonance and they improve the calculated accuracy of their universal properties. A hitherto unanalysed feature found in ultracold-gas experiments3 supports this universal prediction, and it provides the first evidence of four-body recombination (where B+B+B+B form B3+B, B2+B+B or B2+B2).
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converging at large R to the atom–trimer thresholds.
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Acknowledgements
This work was supported in part by the National Science Foundation. We are indebted to N. Mehta and S. Rittenhouse for extensive discussions and for access to their unpublished derivations before publication. We also thank F. Ferlaino, S. Knoop, H.-C. Nägerl and R. Grimm from the Innsbruck group for discussions about their experimental data.
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von Stecher, J., D’Incao, J. & Greene, C. Signatures of universal four-body phenomena and their relation to the Efimov effect. Nature Phys 5, 417–421 (2009). https://doi.org/10.1038/nphys1253
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DOI: https://doi.org/10.1038/nphys1253
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