The purpose of this text is to provide an examination of how the theory of the interaction of atoms and electromagnetic fields has evolved and discuss what new knowledge each step has brought to physics. Of course, not every theoretical innovation can be examined, but the most distinct steps will be highlighted. Three models will be discussed: the Lorentz Oscillator model, the semiclassical model, and the quantized model of atom--field interactions. A two--state atom will be used throughout this work due to its theoretical simplicity.
The Lorentz Oscillator model is classical and may be solved analytically; although this model does not include any quantum mechanical concepts, it will illuminate certain effects whose origin will become clear once the quantum regime has been breached. The semiclassical model quantizes the atom but not the field. This treatment allows one to discover a number of effects which are alien to the classical model and also explains the results of the classical models. The third model quantizes both the atom and the field. This fully quantized system predicts even more interesting effects. From this model one can extrapolate to a number of more advanced systems like the micromaser.
In order to facilitate an understanding of the semiclassical and quantized interaction of a two--state atom and an electromagnetic field, four Pascal applications for the Windows platform have been written: BlochApp, FieldApp, JCApp, and QEDApp. BlochApp simulates the semiclassical model and allows the user to examine the Bloch vector representation. FieldApp simulates a single mode of a quantized electromagnetic field interacting with a reservoir at a given temperature. Both JCApp and QEDApp reexamine the problem in BlochApp with the added complication of the quantized electromagnetic field observed in FieldApp. QEDApp solves this problem rigorously for a two--state atom coupled to a two--state field, while JCApp uses the Jaynes--Cummings model to approximate this interaction and allows the user to simulate large numbers of field states. These applications are meant to form a coherent package that will allow an advanced undergraduate or beginning graduate student to learn about the fascinating problem of atom--field interactions.