We have now derived a number of general properties of a quantized electromagnatic field, and have encountered some useful formalisms for treating certain problems in quantum optics. We have introduced the correlation functions of the field, and we have seen in a general way how they are related to measurements. In selecting examples for illustration we have tended to focus our attention largely on certain idealized quantum states of the field, such as Fock states and coherent states. However, there exists an important class of optical fields with simple properties, the so-called thermal fields, which includes most fields commonly encountered in practice, that has not yet been discussed. These fields are produced by sources in thermal equilibrium, and they exhibit many features that can be treated almost exactly in our formalism. We now turn our attention to such fields.

Blackbody radiation

The density operator

Blackbody radiation is the name given to an electromagnetic field in thermal equilibrium with a large thermal reservoir or heat bath at some temperature T. By definition, such a field is assumed to be coupled to the heat bath, and it is therefore not a strictly free field in the sense of the previous chapters. However, the coupling can be as weak as we wish, and it is well known from the general theory of statistical thermodynamics that the properties of a system with many degrees of freedom in thermal equilibrium (described by a canonical ensemble) are often similar to those of an equivalent isolated system (described by a microcanonical ensemble).