Universal van der Waals physics for three cold atoms near Feshbach resonances



Experimental studies with cold atoms have advanced our understanding of three-body physics, historically a fundamental yet challenging problem. This is because atomic interactions can be precisely varied in strength using magnetically tunable scattering resonances known as Feshbach resonances. Collisions near the unitarity limit, where scattering is maximum, are known to have universal aspects that are independent of short-range chemical details. Away from this limit, many quantum states are expected to be active during a three-body collision, making the collisional observables practically unpredictable. Here we predict three-body ultracold scattering rates by properly building in the pairwise van der Waals interactions plus the multi-spin properties of a tunable Feshbach resonance state characterized by known dimensionless two-body parameters. Numerically solving the Schrödinger equation then quantitatively determines three-atom collisional properties at all interaction strengths without needing adjustable parameters to fit data. Consequently, we can define a new class of van der Waals universality for cold atom three-body phenomena.

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Figure 1: Three-body recombination length ρ3 for Cs atoms near the −11.7 G Feshbach resonance.
Figure 2: Atom–dimer relaxation rate β for Cs atoms near the 25 G Efimov resonance.
Figure 3: Three-body Efimov energy spectrum for Cs atoms near the −11.7 G Feshbach resonance.
Figure 4: Efimov physics for Cs atoms near the 554 G g-wave Feshbach resonance.
Figure 5: Three-body recombination loss rate L3 for85Rb atoms near the 155 G Feshbach resonance.


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The authors acknowledge the support of AFOSR-MURI award FA9550-09-1-0617, partial support from NSF Grant PHY11-25915, and thank C. H. Greene, J. P. D’Incao and J. Wang for discussions on the method and R. Grimm for providing their original data.

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Y.W. and P.S.J. both contributed equally to writing the manuscript. Y.W. planned the project in consultation with P.S.J. and implemented the numerical calculations.

Correspondence to Paul S. Julienne.

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Wang, Y., Julienne, P. Universal van der Waals physics for three cold atoms near Feshbach resonances. Nature Phys 10, 768–773 (2014). https://doi.org/10.1038/nphys3071

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