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.

In this chapter we introduce the Glauber coherent states of a quantized field as eigenstates of the annihilation operator and as displaced vacuum states. The phase-space picture of coherent states is introduced, along with phase-space probability distributions, namely the Q distribution, the P distribution, and the Wigner function, and their interrelations are discussed.

In this chapter we discuss the application of entanglement to quantum optical interferometry and to quantum information processing. Quantum random number generation is discussed. Quantum cryptography is discussed, as is quantum computing. The quantum optical realization of some quantum gates is discussed.

In this chapter we discuss experiments in cavity QED and ion traps. We first discuss the nature of Rydberg atoms which are used in cavity QED experiments. The experimental realization of the Jaynes––Cummings model is discussed, as are the generation of Schrödinger-cat states in dispersive atom––field interactions in cavity QED. The quantum non-demolition measurement is discussed. The realization of the Jaynes––Cummings model in the context of trapped ions is discussed.