Simple quantum-mechanical picture of cold optical collisions

We present a quantum-mechanical study of the dynamics of collisions of cold atoms in a (magneto-) optical trap valid in the linear intensity regime. We find further evidence for a discrepancy with results of the semiclassical optical-Bloch-equation method at lower collision energies and detunings, referred to as ‘‘quantum suppression’’ in previous work. We find a strong dependence on the detuning: for the lowest energies considered the suppression factor ranges from more than three orders of magnitude for Δ=-${\mathrm{\Gamma }}_{\mathrm{at}}$ to a factor 2 at Δ=-10${\mathrm{\Gamma }}_{\mathrm{at}}$. The fraction of atoms surviving at small interatomic distances for a single l value can in good approximation be described by a simple formula in the form of a product of a Landau-Zener excitation function and a WKB survival factor. Summed over partial waves this formula allows a relatively easy calculation of loss rates in a two-channel linear-intensity description. The role of such an approach in a future more complete treatment including hyperfine channels is pointed out.