Efimov Effect in Low-Temperature Trimers

V. Efimov [1] proposed in 1970 that a three-body system with very weak two-particle interactions can form strongly bound states if the two-particle scattering length becomes much larger than the range of the potential. In fact, if the two-body interactions approach zero, the number of resonant three-body states can approach infinity. The helium trimer , first identified in 1977, has been believed to be such a three-body system. In the past two or three years, the field has exploded, with several heavier low-temperature atomic trimers, notably those containing , , , and , having been verified to exhibit the Efimov effect [2].
Given an interatomic potential of the form , let the coupling constant be reduced below , either in concept or by means of some newly developed low-temperature techniques involving Feshbach resonances. It is then found that Efimov trimers are created with binding energies in the millikelvin (mK) range. The green lines represent the energies of these Efimov states as a function of coupling constant. As the temperature is raised these dissociate directly into three free atoms. If, however, is increased, while maintaining the low temperature, the trimers are found to dissociate into dimers+monomers, which occupy the solid green region of the graphic.
The author, in collaboration with L. L. Lohr [3], derived exact solutions for dimers and trimers based on a model in which the interatomic interaction has the form of a Dirac bubble potential, . As shown by Efimov, the precise form of the interatomic potential is not important, only its resonant character. The results derived to construct the graphic can therefore be considered to be of general validity.



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[1] V. Efimov, "Energy Levels Arising from Resonant Two-Body Forces in a Three-Body System," Physics Letters, 33B(8), 1970 pp. 563–564.
[2] F. Ferlaino and R. Grimm, "Forty Years of Efimov Physics: How a Bizarre Prediction Turned into a Hot Topic," Physics 3(9), American Physical Society, Spotlighting Exceptional Research 2010.
[3] L. L. Lohr and S. M. Blinder, "Analytic Representation of the Efimov Effect in the Helium Trimer," Physical Review A 69(6), 2004 064102 pp. 1–4.
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