Creating three-mode entanglement of optical fields via effective coupling to separated atomic ensembles

We present a scheme to generate three-mode entanglement of optical fields based on concurrent interaction with separated atomic ensembles. The inseparability criterion for multimode entanglement [Phys. Rev. A 67 (2003) 052315] is well satisfied in a wide range of relevant parameters, which is sufficient to demonstrate genuine tripartite entanglement. Unlike most of the proposals that the environment will induce decoherence, here we show that the largest correlations of the three cavity modes are insensitive to the cavity decay rate. It is also found that the best correlations can be optimized by the effective coupling constants between the cavity fields and the collective atomic operators.