Quantitative simulation of a magneto-optical trap operating near the photon recoil limit

We present a quantitative model for magneto-optical traps operating on narrow transitions, where the transition linewidth and the recoil shift are comparable. We combine a quantum treatment of the light scattering process with a Monte-Carlo simulation of the atomic motion. By comparing our model to an experiment operating on the $5\rm{s}^2~^1\rm{S}_0 \rightarrow 5\rm{s}5\rm{p}~^3\rm{P}_1$ transition in strontium, we show that it quantitatively reproduces the cloud size, position, temperature and dynamics over a wide range of operating conditions, without any adjustable parameters. We also present an extension of the model that quantitatively reproduces the transfer of atoms into a far off-resonance dipole trap (FORT), highlighting its use as a tool for optimising complex cold atom experiments.