Topical review - Interaction of bimodal fields with few-level atoms in cavities and traps

The spectacular experimental results of the last few years in cavity quantum electrodynamics and trapped-ion 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. This progress has 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, for instance, the Jaynes Cummings model and most of its numerous nonlinear multiphoton generalizations, have been realized or simulated in the laboratory and their dynamic 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 dynamic 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 the parity effect, consists of a high sensitivity to the evenness or oddness of the total number of bosonic excitations.