Dicke state generation using cross-Kerr nonlinearity

In this paper, we propose two ways of Dicke state generation using single photons and weak coherent pulse resorting to Kerr nonlinearities. By interference of two coherent beams, the Dicke state are realized in polarization and photon number degrees of freedom. By performing homodyne detection on the coherent states, the multi-particle entangled Dicke state can be generated with a high probability. The realization of the protocols are more flexible as the phase differences can be easily distinguished during homodyne detection.