  The development of new quantum light sources requires robust and convenient
methods of characterizing their joint spectral properties. Measuring the joint
spectral intensity between a photon pair ignores any correlations in spectral
phase which may be responsible for degrading the quality of quantum
interference. A fully phase-sensitive characterization tends to require
significantly more experimental complexity. Here, we investigate the
sensitivity of the frequency-resolved double-pair emission to spectral phase
correlations, in particular to the presence of a simple form of correlated
phase which can be generated by a chirped pump laser pulse. We observe
interference fringes in the four photon coincidences which depend on the
frequencies of all four photons, with a period which depends on the strength of
their correlation. We also show that phase correlations in the JSA induce
spectral intensity correlations between two signal photons, even when the
corresponding idler photons are not detected, and link this correlation pattern
to the purity of a single signal photon. These effects will be useful in
assessing new photon-pair sources for quantum technologies, especially since we
require little additional complexity compared to a joint spectral intensity
measurement - essentially just the ability to detect at least two photons in
each output port.
