Dynamics of Atom-Mediated Photon-Photon Scattering I: Theory
  The mediated photon-photon interaction due to the resonant Kerr nonlinearity in an inhomogeneously broadened atomic vapor is considered. The time-scale for photon-photon scattering is computed and found to be determined by the inhomogeneous broadening and the magnitude of the momentum transfer. This time can be shorter than the atomic relaxation time. Effects of atom statistics are included and the special case of small-angle scattering is considered. In the latter case the time-scale of the nonlinear response remains fast, even though the linear response slows as the inverse of the momentum transfer. 
M. W. Mitchell and R. Y. Chiao