Magneto-optical trap loading rate dependence on trap depth and vapor density

We study the dependence of the particle loading rate of a rubidium vapor cell magneto-optic trap (MOT). Using a trap depth determination of the MOT that relies on measurements of loss rates during optical excitation of colliding atoms to a repulsive molecular state, we experimentally determine the MOT escape velocity and show that the loading rate scales with escape velocity to the fourth power, or, equivalently, with the square of the trap depth. We also demonstrate that the loading rate is directly proportional to the background rubidium density. We thus experimentally confirm the loading rate model used in the literature since the invention of the MOT. In addition to confirming this long-standing conjecture, we show that the loading rate dependence can be used to reliably infer the trap depth and to tune the relative depth of a MOT (i.e., capture and escape velocities) when the background density is held fixed. The measurements have allowed an experimental determination of the relationship between capture and escape velocities in our MOTs of V sub(c)=1.29(0.12)v sub(e).