We discuss the impact of a finite effective range on three-body systems interacting through a large two-body scattering length. By employing a perturbative analysis in an effective field theory well suited to this scale hierarchy we find that an additional three-body parameter is required for consistent renormalization once range corrections are considered. This allows us to extend previously discussed universal relations between different observables in the recombination of cold atoms to account for the presence of a finite effective range. We show that such range corrections allow us to simultaneously describe the positive and negative scattering-length loss features observed in recombination with 7 Li atoms by the Bar-Ilan group. They do not, however, significantly reduce the disagreement between the universal relations and the data of the Rice group on 7 Li recombination at positive and negative scattering lengths.We discuss the impact of a finite effective range on three-body systems interacting through a large two-body scattering length. By employing a perturbative analysis in an effective field theory well suited to this scale hierarchy we find that an additional three-body parameter is required for consistent renormalization once range corrections are considered. This allows us to extend previously discussed universal relations between different observables in the recombination of cold atoms to account for the presence of a finite effective range. We show that such range corrections allow us to simultaneously describe the positive and negative scattering-length loss features observed in recombination with 7 Li atoms by the Bar-Ilan group. They do not, however, significantly reduce the disagreement between the universal relations and the data of the Rice group on 7 Li recombination at positive and negative scattering lengths.

arXiv:1005.1990Europhysics Letters (EPL)Oct 1, 201031 citations

Universality constraints on three-body recombination for cold atoms: From He4 to Cs133

Eric Braaten, Daekyoung Kang, Lucas Platter

For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for $^{4}\mathrm{He}$ atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the $^{4}\mathrm{He}$ results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to $^{133}\mathrm{Cs}$ atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.For atoms with large scattering length, the dependence of the three-body recombination rate on the collision energy is determined by the scattering length and the Efimov three-body parameters and can be expressed in terms of universal functions of a single scaling variable. We use published results on the three-body recombination rate for $^{4}\mathrm{He}$ atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the $^{4}\mathrm{He}$ results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to $^{133}\mathrm{Cs}$ atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.

arXiv:cond-mat/0612601Physical Review AMay 22, 200716 citations

Three-Body Recombination in One-Dimensional Systems

James R. Macdonald Labs

May 1, 20060 citations

Three-Body Recombination at Thermal and Ultra-low energies

M. Raymond Flannery

APSOct 1, 19980 citations

Universal Analysis of Three-Body Recombination of

^{87}

Rb Atoms

^{4}\mathrm{He}

atoms to constrain the universal functions. We then use those universal functions to calculate the three-body recombination rate for other atoms with large scattering length at nonzero temperature. The constraints from the

^{4}\mathrm{He}

results are strong if the scattering length is near the minimum of the three-body recombination rate at threshold. We apply our results to

^{133}\mathrm{Cs}

atoms with a large positive scattering length, and compare them with experimental results from the Innsbruck group.