We study angular correlations of the radiation emitted by spatially extended sets of atoms. Such correlations result from the fact that the photons are identical quantum particles. We show that the symmetry (or the antisymmetry) alone of the wave function for identical, indistinguishable particles always leads to significant angular correlations and that in full agreement with our intuition, bosons tend to travel in the same direction while fermions tend to travel in opposite directions. In order to quantify these intuitive notions, we introduce—as a measure of angular correlations—the average value of the cosine of the angle between the directions of the momenta of two particles. The angular correlation coefficient is calculated for simple, model wave functions and the results are compared with those obtained from an exactly soluble model describing radiating harmonic oscillators. We find that even though the interaction modifies the exact values of the angular correlation coefficient, the gross features can be obtained from quantum statistics, i.e., from the symmetry of the many-photon wave functions. Moreover, the angular correlations as measured by the average cosine exhibit an almost universal character, at least for a small number of emitting atoms. Finally, we compare angular correlations obtained in quantum electrodynamics with the correlations resulting from the phenomenologically introduced randomness of the phases in the classical description of the electromagnetic field.

• Received 30 April 1990

DOI:https://doi.org/10.1103/PhysRevA.42.2829