The authors present a weak light field, scattering theoretical description of the intensity autocorrelation function for the scattered light from a many-atom (molecule) system. The theory considers both resonant and near-resonant scattering for atoms with many sublevels in both the ground and electronically excited states, and it incorporates the effects of the finite coherence time of the incident radiation. The theory is derived using incident two-photon wave packets with spatial dispersion among the target atoms. Purely anti-bunching contributions arise from single-atom-two-photon scattering and from successive two-atom-two-photon scattering events. However, there are interleaved two-atom-two-photon scattering processes which provide purely bunching contributions since both atoms may be scattering at the same time. Path length differences in the successive two-atom scatterings can also induce some bunching character to the correlation function. The dependence of the risetime and decay of the intensity correlation function upon the atomic excited state lifetimes and the coherence time of the incident light emphasises the correlation between photons which have been coherently and/or incoherently scattered.
The one- and two-photon scattering matrix
S is obtained analytically for a one-dimensional waveguide and a pointlike scatterer with
N excited levels (generalized
V-type atom). We argue that the two-photon scattering matrix contains sufficient information to distinguish between different level structures which are equivalent for single-photon scattering, such as a
V atom with
N=2 excited levels and two two-level systems. In particular, we show that the scattering with the
V-type atom exhibits a destructive interference effect leading to two-photon coupled-resonator-induced transparency, where the nonlinear part of the two-photon scattering matrix vanishes when each incident photon fulfills a single-photon condition for transparency.