Measurement of collisions between rubidium atoms and optically dark rubidium ions in trapped mixtures

We measure the collision-rate coefficient between laser-cooled rubidium (Rb) atoms in a magneto-optical trap (MOT) and optically dark Rb${}^{+}$ ions in an overlapping Paul trap. In such a mixture, the ions are created from the MOT atoms and allowed to accumulate in the ion trap, which results in a significant reduction in the number of steady-state MOT atoms. A theoretical rate-equation model is developed to describe the evolution of the MOT atom number due to ionization and ion-atom collisions, and we derive an expression for the ion-atom collision-rate coefficient. The loss of MOT atoms is studied systematically by sequentially switching on the various mechanisms in the experiment. Combining the measurements with the model allows the direct determination of the ion-atom collision-rate coefficient. Finally, the scope of the experimental technique developed here is discussed.