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

Quantum atom-light interfaces in the gaussian description for spin-1 systems