  The preparation of light pulses with well-defined quantum properties requires
precise control at the individual photon level. Here, we demonstrate exact and
controlled multi-photon subtraction from incoming light pulses. We employ a
cascaded system of tightly confined cold atom ensembles with strong,
collectively enhanced coupling of photons to Rydberg states. The excitation
blockade resulting from interactions between Rydberg atoms limits photon
absorption to one per ensemble and engineered dephasing of the collective
excitation suppresses stimulated re-emission of the photon. We experimentally
demonstrate subtraction with up to three absorbers. Furthermore, we present a
thorough theoretical analysis of our scheme where we identify weak Raman decay
of the long-lived Rydberg state as the main source of infidelity in the
subtracted photon number. We show that our scheme should scale well to higher
absorber numbers if the Raman decay can be further suppressed.
