Photon-number selective group delay in cavity induced transparency

We show that the group velocity of a probe pulse in an ensemble of $\mathrm{\Lambda }$-type atoms driven by a quantized cavity mode depends on the quantum state of the input probe pulse. In the strong-coupling regime of the atom-cavity system the probe group delay is photon number selective. This can be used to spatially separate the single photon from higher photon-number components of a few-photon probe pulse and thus to create a deterministic single-photon source.