8. Single atoms moving in a high-finesse cavity

This chapter explores some of the consequences that result from the condition of high finesse and small waist or, alternatively, high-quality factor and small volume. The chapter introduces the basic ingredients of the quantum theory describing the interaction of a single atom with a light field containing at most a few photons. Detecting a single atom in a high-finesse cavity supporting a mode with a small waist is particularly interesting for a slowly moving atom. Such an atom can interact with a large number of consecutive photons in the cavity before moving a significant distance. It must be realized that a slow atom does not move unperturbed through the light field. Instead, it experiences light forces, which originate from the exchange of photons between the atom and the cavity field. It can be expected that in a small, high-finesse cavity these light forces are different from those in free space. The atom-cavity coupling leads to a rich and interesting dynamics of both the cavity variables and the atomic variables. A few experimental considerations concerning the cavity design are discussed and an outlook is given on the prospects of this research and some possible applications.