Control of ultraslow inelastic collisions by Feshbach resonances and quasi-one-dimensional confinement

Inelastic collisions of ultracold atoms or molecules are analyzed using very general arguments. In free space, the deactivation rate can be enhanced or suppressed together with the scattering length of the corresponding elastic collision via a Feshbach resonance, and by interference of deactivation of the closed and open channels. In reduced dimensional geometries, the deactivation rate decreases with decreasing collision energy and does not increase with resonant elastic scattering length. This has broad implications; e.g., stabilization of molecules in a strongly confining two-dimensional optical lattice, since collisional decay of excited states due to inelastic collisions is suppressed. The relation of our results to the Lieb-Liniger model for bosonic atoms is addressed.