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The quantum state for spontaneous parametric down-conversion was evaluated to include information about the transverse spatial characteristic of the down-conversion fields. This state was used to calculate the angular spectrum of down-conversion in the case of both single-channel and coincidence measurements, while retaining the characteristic nonclassical correlations. Actual transverse profiles for typical experimental parameters were evaluated numerically and measurements were performed with results that compared well with the numerical calculation. This theoretical spatial model was then applied nonrigorously to the case of induced coherence without induced emission. The theoretical results implied that there was a reduction in the degree of induced coherence due strictly to the spatial distribution of the down-conversion beams. This was interpreted as a result of increased distinguishability of the overlapping idler photons. Measurements were conducted which support these results qualitatively. In addition, the present theory explained an unexpected quantitative discrepancy between second- and fourth-order visibilities in previous induced-coherence experiments. This discrepancy was interpreted phenomenologically as a difference between intrinsic and nonintrinsic indistinguishability, and some implications towards quantum measurement theory and the role of the observer were suggested.
Grayson et al. (Fri,) studied this question.