The spectacular experimental results of the last few years in cavity quantum
electrodynamics and trapped ions research has led to very high level laboratory
performances. Such a stimulating situation essentially stems from two decisive
advancements. The first is the invention of reliable protocols for the
manipulation of single atoms. The second is the ability to produce desired
bosonic environments on demand. These progresses have led to the possibility of
controlling the form of the coupling between individual atoms and an arbitrary
number of bosonic modes. As a consequence, fundamental matter-radiation
interaction models like, for instance, the JC model and most of its numerous
nonlinear multiphoton generalizations, have been realized or simulated in
laboratory and their dynamical features have been tested more or less in
detail. This topical paper reviews the state of the art of the theoretical
investigations and of the experimental observations concerning the dynamical
features of the coupling between single few-level atoms and two bosonic modes.
In the course of the paper we show that such a configuration provides an
excellent platform for investigating various quantum intermode correlation
effects tested or testable in the cavity quantum electrodynamics and trapped
ion experimental realms. In particular we discuss a mode-mode correlation
effect appearing in the dynamics of a two-level atom quadratically coupled to
two bosonic modes. This effect, named parity effect, consists in a high
sensitivity to the evenness or oddness of the total number of bosonic
excitations.Comment: Topical Review. To appear on J. Mod. Op
