SPATIAL EFFECTS IN 2-BEAM AND 4-BEAM INTERFERENCE OF PARTIALLY ENTANGLED BIPHOTONS

Fourth-order interference patterns of biphotons generated by type-I sp ontaneous parametric downconversion are examined for beams with partia l angular and spectral entanglement, both for degenerate and nondegene rate constituent photons. Two-beam configurations using a single beam- splitter interferometer and a Mach-Zehnder interferometer are explicit ly studied, as are four-beam configurations using pairs of beam splitt ers and Mach-Zehnder interferometers. The interference pattern general ly comprises a number of harmonic functions of the path-length differe nce with frequencies and visibilities that usually depend on direction , and may have a finite or infinite duration (fourth-order coherence l ength). The relation between the visibility and the spectral indisting uishability of the two beams is established. Certain components of the interference pattern are independent of direction so that they are no t washed out by the use of apertures of finite size.