Stationary distributions in the atom-on-demand problem

In this note a probability model for the number of atoms in a magneto-optical trap is suggested. We study an ergodic Markov chain for the number of atoms in the trap under a feedback regime for different load distributions. Formulas for the stationary distribution of the process are derived in several cases. They can be used to adjust the loading rate of atoms to maximize the probability of a single atom in the trap. Approximate optimal regimes are found.