  The microscopic theory of superconductivity raised the disruptive idea that
electrons couple through the elusive exchange of virtual phonons, overcoming
the strong Coulomb repulsion to form Cooper pairs. Light is also known to
interact with atomic vibrations, as for example in the Raman effect. We show
that photon pairs exchange virtual vibrations in transparent media, leading to
an effective photon-photon interaction identical to that for electrons in BCS
theory of supercondutivity, in spite of the fact that photons are bosons. In
this scenario, photons may exchange energy without matching a quantum of
vibration of the medium. As a result, pair correlations for photons scattered
away from the Raman resonances are expected to be enhanced. Experimental
demonstration of this effect is provided here by time correlated Raman
measurements in different media. The experimental data confirm our theoretical
interpretation of a photonic Cooper pairing, without the need for any fitting
parameters.
