  A powerful method to interface quantum light with matter is to propagate the
light through an ensemble of atoms. Recently, a number of such interfaces have
emerged, most prominently Rydberg ensembles, that enable strong nonlinear
interactions between propagating photons. A largely open problem is whether
these systems produce exotic many-body states of light and developing new tools
to study propagation in the large photon number limit is highly desirable.
Here, we provide a method based on a "spin model" that maps quasi
one-dimensional (1D) light propagation to the dynamics of an open 1D
interacting spin system, where all photon correlations are obtained from those
of the spins. The spin dynamics in turn are numerically solved using the
toolbox of matrix product states. We apply this formalism to investigate vacuum
induced transparency, wherein the different photon number components of a pulse
propagate with number-dependent group velocity and separate at output.
