Photon-number dependent cavity vacuum induced transparency and single photon separation

We investigate photon-number dependent cavity vacuum induced transparency and magneto-optical rotation (MOR) in a cavity quantum electrodynamics system, which consists of two cavities and an ensemble of Λ-type atoms. We demonstrate that the probe photon coupled into one cavity can be transferred to the mode of another cavity via coherent Raman scattering. The transmission, the phase shift, as well as the vacuum Rabi splitting therefore strongly depend upon the probe photon number coupled into the cavity. The photon number dependent cavity vacuum induced transparency can be extended into four-level tripod atoms, leading to photon-number dependent MOR. This can be used to separate the single photon from higher photon number components in the direction of polarization and create a deterministic single photon source.