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Since the photon box gedanken experiments of several of the founding fathersof modern physics, considerable progress has been made in differentiating thequantum and classical worlds. In this pursuit, the cavity as an open quantumsystem has been indispensable. From the quantization of the atom and fieldwithin a superconducting cavity, a unique realm of EPR type entanglement hasemerged. In this way, dynamical evolution of the system in the strong couplingregime is intimately tied with the coupling of an atom with a single resonantor non-resonant mode within the cavity. More specifically, the cavity can beprepared so that the atom is detected in a desired state. Here, the essentialsof the strong coupling regime of Cavity Quantum Electrodynamics (QED) arereviewed for cavities tuned with a single atomic transition. A briefintroduction of the systems is followed by an approach of the more strikingeffects, leading towards Ramsey Interferometry and Quantum Non-Demolitionmeasurements as means for quantum gate protocol. Because the integrity of theatom and photon states is important for the advancement of quantum computation,a brief discussion of the decoherence problems is also presented. This documentis meant to introduce the topic in a way that makes it easily accessible tothose working in closely related areas of physics, and to highlight keyapplications and some basic questions concerning decoherence and themeasurement problem.

A Quick Introduction to the strong coupling regime of Cavity Quantum Electrodynamics: applications and fundamental quantum theory