ABSTRACT
This chapter culminates with a discussion of the photon wave mechanical picture of the correlated spontaneous emissions from a three-level atom. The photon spin entanglement of the two-photon cascade J = 0→ J = 1→ J = 0 is briefly analyzed in Sec. 32.5, paying attention to the correlations in the spin state space. Measurements are always carried out in direct space, and for this reason alone it is of interest to study the space-time correlations of the cascade process. The existing theories focus attention on the far-field correlations [214]. In the far field the spatial extension of the rim zone of the atom is unimportant. However, if one imagines that the two detectors needed to measure the second-order correlation matrix at two different space-time points are moved into the rim zone of the atom, the lack of spatial localization of the transverse photons mixes with the quantum mechanical entanglement phenomenon. The standard theory of two-photon cascade entanglement is extended to the domain of near-field electrodynamics by relating the final two-photon state in Hilbert space to photon wave mechanics in direct space.
