Feshbach resonances in a quasi-two-dimensional atomic gas

Strongly confining an ultracold atomic gas in one direction to create a quasi-two-dimensional system alters the scattering properties of this gas. We investigate the effects of confinement on Feshbach scattering resonances and show that strong confinement results in a shift in the position of the Feshbach resonance as a function of the magnetic field. This shift, as well as the change of the width of the resonance, is computed. We find that the resonance is strongly damped in the thermal gas, but in the condensate the resonance remains sharp due to many-body effects. We introduce a two-dimensional model system, suited for the study of resonant superfluidity and having the same scattering properties as the tightly confined real system near a Feshbach resonance. Exact relations are derived between measurable quantities and the model parameters.