  We study a class of quantum Markov processes that, on the one hand, is
inspired by the micromaser experiment in quantum optics and, on the other hand,
by classical birth and death processes. We prove some general geometric
properties and irreducibility for non-degenerated parameters. Furthermore, we
analyze ergodic properties of the corresponding transition operators. For
homogeneous birth and death rates we show how these can be fully determined by
explicit calculation. As for classical birth and death chains we obtain a rich
yet simple class of quantum Markov chains on an infinite space, which allow
only local transitions while having divers ergodic properties.
