  We investigate the interaction between non-classical light with a tunable
multiphoton component and a highly nonlinear medium based on cold Rydberg
atoms. The non-classical field emitted by a DLCZ quantum memory is stored using
Rydberg electromagnetically induced transparency, experiencing strong nonlinear
response due to the dipole blockade. We show that the storage efficiency in the
Rydberg ensemble decreases as function of the multiphoton strength of the input
field, as a result of the nonlinearity. We also show that the autocorrelation
function $g^{(2)}(0)$ of the retrieved field after storage in the Rydberg state
is considerably reduced, leading to the first demonstration of single photon
filtering with non-classical input light. Finally, we develop a simple
simulation that allows us to model the effect of our medium on the input state.
This work is a step towards matter-mediated photon-photon interactions with
non-classical light.
