Simple Theoretical Models for Resonant Cold Atom Interactions

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.