The structure of diatomic molecules is discussed in this chapter. The electronic structure of diatomic molecules is then discussed in detail. The coupling of the orbital and spin angular momenta of electrons and the angular momentum associated with nuclear rotation are discussed, with an emphasis on Hund’s cases (a) and (b). The rotational wavefunctions for diatomic molecules in the limits of Hund’s cases (a) and (b) and in the case intermediate between Hund’s cases (a) and (b) are then discussed in detail. For molecules that are of importance in combustion diagnostics, such as OH, CH, CN, and NO, the electronic levels are intermediate between Hund’s cases (a) and (b). We use Hund’s case (a) as the basis wavefunctions, and linear combinations of these wavefunctions are used to represent wavefunctions for electronic levels intermediate between cases (a) and (b). The choice of case (a) wavefunctions as the basis set is typical in the literature although case (b) wavefunctions can also be used as a basis set.

Raman scattering spectroscopy is widely used in analytical chemistry, for structural analysis of materials and molecules and, most importantly for our purposes, as a gas-phase diagnostic technique. Raman scattering is a two-photon scattering process, and the mathematical treatment of Raman scattering is very similar to the mathematical treatment of two-photon absorption. Many of the molecules of interest for quantitative gas-phase spectroscopy are diatomic molecules with non-degenerate 1Σ ground electronic levels, including N2, CO, and H2. In this chapter, the theory of Raman scattering is developed based on Placzek polarizability theory and using irreducible spherical tensor analysis. Herman–Wallis effects are discussed in detail. The chapter concludes with detailed examples of Raman scattering signal calculations.

This chapter starts with the quantization of a single mode of the electromagnetic field and introduces the photon annihilation and creation operators. The photon number states are introduced. The field quadrature operators are introduced and quantum fluctuations are discussed. Multimode fields are then discussed. Thermal fields are introduced and vacuum fluctuations and the zero-point energy are discussed. The quantum phase of a quantized single-mode field is introduced.

In this chapter we discuss the interaction of radiation with matter, the latter taken to be a two-level atom. We consider interactions with both classical and quantum fields. We first introduce the dipole approximation and the rotating-wave approximation, and then study the Rabi model of a classical field interacting with a two-level atom. We next introduce the quantized field interaction with matter and discuss absorption, spontaneous emission, and stimulated emssion. We then discuss the long-time evolution of a single-mode field with a two-level atom –– the Jaynes––Cummings model.

In this chapter we first discuss the classical coherence functions and then introduce the quantum coherence functions. We present a quantum mechanical discussion of Young’s interference experiment. The Hanbury-Bown and Twiss experiment is discussed, along with higher-order coherence functions.

In this chapter we discuss nonclassical states of light. These include squeezed states of light, states with sub-Poissonian statistics, two-mode squeezed states, photon antibunching, superpositions of coherent states of light –– these being the Schrödinger-cat states. Also discussed in this chapter are the nonclassical states generated by the addition and subtraction of photons.

In this chapter we discuss optical tests of quantum mechanics. These include the Hong––Ou––Mandel effect, quantum erasure, induced coherence, superluminal tunneling of photons, violations of Bell’s inequality, and Franson’s experiment.

In this chapter we discuss the effects of losses on quantum optical systems. We discuss quantum jumps and master equations. We introduce the notion of using fictitious beam splitters to model losses. We introduce the decoherence of pure quantum mechanical states into a statistical mixture.

This chapter briefly describes the scope and aims of the book and the history of quantum optics as a science in its own right.