Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box

2

Fiat Lux! A free tasting of field quantization

God said

and then there was light!¹

—Popular physics joke²

This chapter is an introduction to the quantization of the electromagnetic radiation field. Here we deal with the simple case of radiation alone, without any sources or sinks that its interaction with matter generates. One of the reasons that the quantization of the free radiation field is simpler than that of the field with sources is that there is no need to use electromagnetic potentials and to choose a gauge.³

In the next section we review the canonical quantization method. This is one of the finest “wines” in physics. To help even newcomers appreciate it fully, we establish the connection with the more familiar elementary quantum mechanics formalism by using canonical quantization to derive the Schrödinger equation description of a nonrelativistic particle from classical mechanics. In Section 2.2 we explain why it is only the radiation field, rather than the total field, that is quantized. In Section 2.3 we review cavities. Rather than just presenting a formal calculation of cavity modes (such a calculation is done in Appendix A), we discuss the idea of a cavity or resonator and the physics it involves. We start with an elementary introduction to the phenomenon of resonance. Then we go on to show how the features we associate with resonators emerge when an oscillating ...