Possibility of efficient generation of multiphoton entangled states using a one-dimensional nonlinear photonic crystal

A rigorous quantum theory for the generation of multiphoton entangled states based on two consecutive three-frequency interactions of waves in a one-dimensional nonlinear photonic crystal is developed using the field expansion and differentiation methods. The three-photon correlation coefficient and the average photon numbers generated in the structure are calculated. All order expansion terms are included in the calculation. The generation conditions for multiphoton entangled states in such a structure are also analyzed. It is shown that the created photons in the present structures obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state. This means the nonlinear photonic crystal can be applied as a highly efficient source of an entangled multiphoton for highly integrated all-optical circuits.