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

Abstract

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 $2M+1$ Fock states.