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Abstract

The atom is the most elementary constituent of any model that describes the quantum nature of light–matter interaction. Because atoms emit and absorb light at well-defined frequencies, nineteenth century scientists thought of them as collections of harmonically oscillating electric dipole moments or EHDs. In the language of modern physics, the latter represent dipolar transitions among the various quantum mechanical states of an atom.

In a strict definition, the field of quantum optics deals with problems that not only require the quantization of matter but also of the electromagnetic field, with examples such as (i) generation of squeezed light or Fock states, (ii) strong coupling of an atom and a photon, (iii) entanglement of a photon with an atom and (iv) Casimir and van der Waals forces. There are also many other important topics that have been discussed within the quantum optics community but do not necessarily require a full quantum electrodynamic (QED) treatment. Examples are (i) cooling and trapping of atoms, (ii) precision spectroscopy and (iii) modification of spontaneous emission.

The simple picture of a TLS as an EHD remains very insightful and valuable to this day. Indeed, much of what we discuss in this chapter has to do with the interplay between the quantum and classical mechanical characters of dipolar oscillators. For instance, the extinction cross-section of a TLS, given by 3λ2/2π, can be derived just as well using quantum mechanics [70] or classical optics [234]. Another example, albeit more subtle, concerns the spontaneous emission rate.