Quantum dynamics of interacting modes in the process of intracavity subharmonic generation

The dynamics of correlation between fluctuations of the number of photons of interacting modes is investigated for the process of intracavity subharmonic generation. It is demonstrated that this correlation strongly depends on the nonlinear mode coupling coefficient. For small values of the coupling coefficient, the correlation between fluctuations of the number of photons is small. With an increase in the coupling coefficient, the correlation increases (the state of subsystems becomes entangled) and, starting from a particular value of the coupling coefficient, starts to decrease with further increase in the coupling coefficient, gradually approaching zero (entanglement of subsystem states decreases). The quantum dynamics of the number of photons, quantum entropy, and Wigner function of the stationary state of the fundamental and subharmonic modes is investigated. It is demonstrated that the dynamics of these quantities also strongly depends on the coupling coefficient of the interacting modes. We show that, for large values of the mode coupling coefficient and long interaction times, the subharmonic mode becomes localized in a two-component state with equal probabilities of finding it in each component. Quantum entropy of this state is smaller than maximum entropy of the two-component state equal to ln2, which suggests that quantum-mechanical interference takes place between the subharmonic mode components.