We present a detailed theoretical analysis of a Fock-state filter based on the photon-number dependent group delay in cavity induced transparency proposed in Phys. Rev. Lett. 105, 013601 (2010). We derive a general expression for the propagation velocity of different photon-number components of a light pulse interacting with an optically dense ensemble of three-level atoms coupled to a resonator mode under conditions of cavity induced transparency. These predictions are compared to numerical simulations of the propagation of few photon wave packets, and an estimation for experimental realization is made.
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