  We derive an effective Hamiltonian for the nonlinear process of parametric
down conversion in the presence of absorption. Based upon the Green function
method for quantizing the electromagnetic field, we first set up Heisenberg's
equations of motion for a single atom driven by an external electric field and
in the presence of an absorbing dielectric material. The equations of motion
are then solved to second order in perturbation theory which, in rotating-wave
approximation, yields the standard effective interaction Hamiltonian known from
free-space nonlinear optics. In a second step, we derive the local-field
corrected Hamiltonian for an atom embedded in a dielectric host medium, i.e. a
nonlinear crystal. Here we show that the resulting effective Hamiltonian is
trilinear in the electric and noise polarization fields, and is thus capable of
describing nonlinear noise processes. Furthermore, it reduces to the
phenomonological nonlinear Hamiltonian for the cases where the noise
polarization field, and hence absorption, vanishes.
