Probing the unitarity limit at low laser intensities

We show how photoassociation (PA) near a magnetically tuned Feshbach resonance can probe the unitarity limit at low laser intensities. This limit occurs when the scattering matrix element in the PA process reaches its quantum limit of one, and is usually difficult to access, requiring large laser intensities. We show how giant enhancements of the PA rate in the vicinity of a Feshbach resonance can reach it, and we predict the appearance of new features with varying magnetic fields and laser intensities. We investigate these effects for a Bose gas of Li-7 atoms at temperatures near quantum degeneracy and give a simple analytical model. We discuss potential applications of our results, obtained without adjustable parameters, to high-precision spectroscopy.