  Photons interact with each other in condensed matter through the same
mechanism that forms Cooper pairs in superconductors -- the exchange of virtual
phonons [PRL 119, 193603 (2017)]. It is however unclear which consequences of
this interaction will be observable and potentially lead to further analogy
with superconductivity. We investigate the energy, momentum and production rate
of correlate Stokes-anti-Stokes (SaS) photons in diamond and other transparent
media, experiencing properties akin to those of electronic Cooper pairs. The
rate of correlated SaS production depends on the energy shifts of the pair,
which in the BCS theory determines whether there should be an attractive or
repulsive interaction. With this view, we only observe correlated SaS in the
case of attractive interactions. While traditional photon-phonon collisions
scatter light in all directions, the correlated SaS photons follow the same
path as the noninteracting laser. The observed correlated SaS photon pairs are
rare, but our model indicates paths to achieve higher interaction energies.
