  Since the photon box gedanken experiments of several of the founding fathers
of modern physics, considerable progress has been made in differentiating the
quantum and classical worlds. In this pursuit, the cavity as an open quantum
system has been indispensable. From the quantization of the atom and field
within a superconducting cavity, a unique realm of EPR type entanglement has
emerged. In this way, dynamical evolution of the system in the strong coupling
regime is intimately tied with the coupling of an atom with a single resonant
or non-resonant mode within the cavity. More specifically, the cavity can be
prepared so that the atom is detected in a desired state. Here, the essentials
of the strong coupling regime of Cavity Quantum Electrodynamics (QED) are
reviewed for cavities tuned with a single atomic transition. A brief
introduction of the systems is followed by an approach of the more striking
effects, leading towards Ramsey Interferometry and Quantum Non-Demolition
measurements as means for quantum gate protocol. Because the integrity of the
atom and photon states is important for the advancement of quantum computation,
a brief discussion of the decoherence problems is also presented. This document
is meant to introduce the topic in a way that makes it easily accessible to
those working in closely related areas of physics, and to highlight key
applications and some basic questions concerning decoherence and the
measurement problem.
