We present a full quantum mechanical three dimensional theory
describing an electromagnetic field interacting with an ensemble of
identical atoms. The theory is constructed such that it describes
recent experiments on light-matter quantum interfaces, where the
quantum fluctuations of light are mapped onto the atoms and back
onto light. We show that the interaction of the light with the
atoms may be separated into a mean effect of the ensemble and a
deviation from the mean. The mean effect of the interaction
effectively give rise to an index of refraction of the gas. We
formally change to a dressed state picture, where the light modes
are solutions to the diffraction problem, and develop a perturbative
expansion in the fluctuations. The fluctuations are due to quantum
fluctuations as well as the random positions of the atoms. In this
perturbative expansion we show how the quantum fluctuations are
mapped between atoms and light while the random positioning of the
atoms give rise to decay due to spontaneous emission. Furthermore we
identify limits, where the full three dimensional theory reduce to
the one dimensional theory typically used to describe the
interaction.