Chapter 3 discusses the interaction Hamiltonian, which determines the way that light interacts with matter. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. The partial successes of perturbation theory are compared with predictions of an “exact” method of calculating the occupation probabilities of various atomic states. The “exact” method is shown to fail, establishing the need for improved approaches that yield correct results in later chapters. The density matrix is introduced as a tool for describing not only the populations of atomic energy levels but also the coherence that can be created and lost during the dynamic evolution of atoms in time. A vector model based on the Bloch vector is presented as a useful way of picturing coherent atom–field interactions in an optical “spin” space, which proves to be particularly useful in understanding multiple-pulse interactions. Mechanisms are described that cause line broadening in optical spectroscopy, such as the Doppler effect. In preparation for the extensive use in later chapters of models based on only two or three energy levels, it is also shown that multi-level real atoms can experimentally be converted into two-level systems for strict comparisons with theory.
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