  We extend the covariance-matrix description of atom--light quantum
interfaces, originally developed for real and effective spin-1/2 atoms, to
include "spin alignment" degrees of freedom. This allows accurate modeling of
optically-probed spin-1 ensembles in arbitrary magnetic fields. We also include
technical noise terms that are very common in experimental situations. These
include magnetic field noise, variable atom number and the effect of magnetic
field inhomogeneities. We demonstrate the validity of our extended model by
comparing numerical simulations to a free--induction decay (FID) measurement of
polarized $^{87}$Rb atoms in the $f = 1$ ground state. We qualitatively and
quantitatively reproduce experimental results with all free parameters of the
simulations fixed. The model can be easily extended to larger spin systems, and
adapted to more complicated experimental situations.

Quantum Physics