  We present a model which describes coherent and incoherent processes in
continuous-variable atom-light interfaces. We assume Gaussian states for light
and atoms and formulate the system dynamics in terms of first and second
moments of the angular momentum operators. Spatial and temporal inhomogeneities
in light and atom variables are incorporated by partitioning the system into
small homogeneous segments. Furthermore, other experimental imperfections as
for instance limited detector time-resolution and atomic motion are simulated.
The model is capable of describing many experimental situations ranging from
room temperature vapor cells to sub-mK atomic clouds. To illustrate the method,
we calculate the effect of detector time-resolution, spatial inhomogeneities
and atomic motion on the spin squeezing dynamics of rubidium 87 on the D2
transition.
