Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing

We propose a scheme to achieve multiparty entanglement with perfectly efficient, ultraslow, multichannel pairwise four-wave mixing (FWM). A cold atomic medium is illuminated with an  N -mode continuous-wave (cw) control laser to produce coherent mixtures of excited states. An ultraslowly propagating, single-photon quantum probe field completes multichannel, pairwise FWM, creating a depth dependent entanglement of  N  Fock states. We show explicitly that this scheme can be utilized to realize an  N -party entangled state of ultraslowly propagating quantized fields. In particular, we give the explicit analytical expression of a three-party W-state propagating at an ultraslow group velocity, and the numerical results of a multiparty W state of  2 M +1  Fock states