Simple models of decaying Feshbach resonances

Scattering properties of ultracold atoms can be controlled using Feshbach resonances, which can be created using magnetic, optical or radio-frequency (rf) coupling of the colliding pair to a bound state. In the lossless case, the scattering length diverges at the resonance. However, in the presence of losses the scattering length has a range limited by the rate of decay. We study decaying resonances with both rigorous calculations and simple, intuitive models. We focus on rf-induced resonances for $^{6}$Li, in which losses are created by rf coupling to several energetically lower channels. We show that creating a resonance by coupling to a broad, near-threshold molecular state can provide useful control with low rf power and manageable losses.