Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is studied. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, of the quantum entropy and of the Wigner function of the stationary states of the fundamental mode and of the third subharmonic mode are also studied. It is found that the dynamics of these values are highly dependent on the value of the coupling coefficient of the interacting modes. In the region of large interaction times, for large values of the coupling coefficient of the modes, it is shown that the third subharmonic mode localizes in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which shows presence of quantum mechanical interference between the components of the state of third subharmonic mode