Properties of quantized electromagnetic fields

Galina A. Nemova

Janik Wolters

In this chapter some properties of the unperturbed quantized electromagnetic field modes described by HˆR (Eq. 2.58) are investigated. As the operators for different modes l commute, and the Hamiltonian HˆR does not mix different modes, all modes can be treated as independent. Thus, for simplicity it is assumed that only a single mode l is occupied. In the next section, some observables of the electromagnetic field modes, namely the electric field operator Eˆ and the magnetic field operator Bˆ are introduced. Later on, in Section 3.2 the eigenvectors of HˆR and the corresponding energy eigenvalues are treated, while the important class of coherent states is revised in Section 3.3. The last Section 3.4 of this chapter is dedicated to the density of photon states.

G. Grynberg, Alain Aspect, Claude Fabre +1 more

Many processes, including absorption and stimulated emission occurring in lasers, can be handled using a semi-classical model for the atom–radiation interaction, in which the matter is given a quantum description, but the radiation is represented as a classical electromagnetic field (see Chapter 2). There are other phenomena that cannot be adequately described without quantizing the radiation. For example, it has been known since the 1930s that spontaneous emission can only be treated correctly using a fully quantum framework for the interaction, in which both the matter and the radiation are quantized, as we shall see in Chapter 6. However, it was not until the 1970s that situations were found in which a free electromagnetic field , far from sources, exhibited properties and behaviour that could not be described by a classical field, but which could be perfectly well interpreted in terms of a quantized field. This chapter is devoted to the quantization of the free electromagnetic field, far from the charges and currents sourcing it. This free electromagnetic field will be called radiation , and in Chapter 6 we shall specify exactly what is meant by radiation when sources are present. The canonical quantization procedure used here starts from a description of the classical dynamics of the field in the framework of the Hamiltonian formalism, the basic features of which are discussed in Section 4.1.

Прохоров Лев Васильевич

Kuniaki Matsuo

Xin Ma, William Rhodes

We show that the approach by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)] to construct a phase operator through a limiting procedure does not give a satisfactory description of the phase properties of the quantized electromagnetic field. We refute the claim that their approach predicts the same results of physical experiments on phase properties as the conventional Hilbert space approach. Their procedure could only be used as a definition of the phase, but it is not a good definition because the ``phase'' states they used to construct their ``phase'' operator are not of precisely defined phase contrary to their assertion.