Efficient atomic and photonic multipartite W state concentration via photonic faraday rotation

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