Stokes-anti-Stokes correlated photon properties akin to photonic Cooper pairs

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.