Laser experiments with single atoms and the test of basic quantum phenomena

In this paper, recent experiments of our group performed with single atoms in cavities and traps are summarized. In the first part, experiments with the one-atom maser are described dealing with the generation of number states of the photon field. In the second part of the paper, the spectroscopy of a single trapped In⁺ ion is discussed being performed with the aim of realizing a new frequency standard in the optical range.