In this article a Markov chain for the distribution of single atoms is suggested and studied. We explore a recursive model for the number of atoms present in a magneto-optical trap under a feedback regime with a Poisson-distributed load. Formulas for the stationary distribution of this process are derived. They can be used to adjust the loading rate of atoms to maximize the proportion of time that a single atom spends in the trap. The (approximate) optimal regime for the Poisson loading and loss processes is found.