Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with $^{87}$ Rb, $^{85}$ Rb, $^{40}$ K, and $^{6}$ Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.Magnetically tunable scattering resonances have been used with great success for precise control of s-wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with $^{87}$Rb, $^{85}$Rb, $^{40}$K, and $^{6}$Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.

Sep 1, 200611 citations

Simple Theoretical Models for Resonant Cold Atom Interactions

Paul S. Julienne, Bo Gao

Magnetically tunable scattering resonances have been used with great success for precise control of s‐wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87Rb, 85Rb, 40K, and 6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.Magnetically tunable scattering resonances have been used with great success for precise control of s‐wave scattering lengths in ultracold atomic collisions. We describe relatively simple yet quite powerful analytic treatments of such resonances based on the analytic properties of the van der Waals long range potential. This theory can be used to characterize a number of properties of specific resonances that have been used successfully in various experiments with 87Rb, 85Rb, 40K, and 6Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.

arXiv:physics/0609013AIP conference proceedingsJan 1, 200623 citations

A Quantum Model of Feshbach Resonances

Raffaele Carlone, M. Correggi, D. Finco +1 more

arXiv:1901.08282Annales Henri PoincaréJun 4, 20193 citations

Simple models of decaying Feshbach resonances

Thomas M. Hanna, Eite Tiesinga, Paul S. Julienne

APSMar 1, 20100 citations

Analytical model of overlapping Feshbach resonances

Krzysztof Jachymski, Paul S. Julienne

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled-channel calculations for several cases of overlapping resonances in the collisions of two ${}^{7}$ Li atoms or two Cs atoms.Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled-channel calculations for several cases of overlapping resonances in the collisions of two ${}^{7}$Li atoms or two Cs atoms.

arXiv:1308.0681Physical Review ANov 6, 201337 citations

^{87}

Rb,

^{85}

Rb,

^{40}

K, and

^{6}

Li. Optical Feshbach resonances are also possible and may be practical with narrow intercombination line photoassociative transitions in species like Sr and Yb.

{}^{7}

Li atoms or two Cs atoms.