  In light matter interfaces based on the Faraday effect quite a number of
quantum information protocols have been successfully demonstrated. In order to
further increase the performance and fidelities achieved in these protocols a
deeper understanding of the relevant noise and decoherence processes needs to
be gained. In this article we provide for the first time a complete description
of the decoherence from spontaneous emission. We derive from first principles
the effects of photons being spontaneously emitted into unobserved modes. Our
results relate the resulting decay and noise terms in effective equations of
motion for collective atomic spins and the forward propagating light modes to
the full atomic level structure. We illustrate and apply our results to the
case of a quantum memory protocol. Our results can be applied to any suitable
atomic species, and the general approach taken in this article can be applied
to light matter interfaces and quantum memories based on different mechanisms.
