Atomic and photonic entanglement concentration via photonic Faraday rotation

We propose two alternative entanglement concentration protocols (ECPs) using the Faraday rotation of photonic polarization. Through the single-photon input-output process in cavity QED, it is shown that the maximally entangled atomic (photonic) state can be extracted from two partially entangled states. The distinct feature of our protocols is that we can concentrate both atomic and photonic entangled states via photonic Faraday rotation, and thus they may be universal and useful for entanglement concentration in the experiment. Furthermore, as photonic Faraday rotation works in low-$Q$ cavities and only involves virtual excitation of atoms, our ECPs are insensitive to both cavity decay and atomic spontaneous emission.