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.

Chapter 18 covers non-parametric methods and includes the following specific topics, among others: parametric versus non-parametric methods, chi-square distribution, chi-square goodness of fit test, chi-square test of independence, Fisher’s exact test, Wilcoxon sign test, Mann–Whitney U-test, Wilcoxon’s rank sum test, and Kruskal–Wallis analysis of variance.

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.

Chapter 4 covers the re-expression or transformation of variables and includes the following specific topics, among others: linear and nonlinear transformations, standard scores, z-scores, recoding variables, combining variables, data management fundamentals, and the importance of the .do-file.

Chapter 10 covers inferences involving the mean of a single population when σ is known and includes the following specific topics, among others: estimating the population mean, interval estimation, confidence intervals, hypothesis testing and interval estimation, effect size, type II error, and power.

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.

Chapter 19 covers customizing and exporting tables to Microsoft Word and Excel using the new table command and includes how to customize one-way tables, two-way tables, tables of univariate summary statistics, correlation tabes, and regression tables, and how to export them to Microsoft Word and Excel.

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