Three-Mode Entangled States of the Field in the Process of Nondegenerate Parametric Decay in an Optical Resonator

For the process of non-degenerate parametric decay in an optical resonator, in which a quantum with energy $$\hbar {{{{\omega }}}_{3}}$$ decays into two quanta with energies $$\hbar {{{{\omega }}}_{2}}$$ and $$\hbar {{{{\omega }}}_{1}}$$ , where $$\hbar {{{{\omega }}}_{3}} = \hbar {{{{\omega }}}_{2}} + \hbar {{{{\omega }}}_{1}}$$ is the possibility of forming entangled states of the field by variables of the number of photons between interacting modes of the optical system is investigated. For this purpose, we investigated the dynamics of normalized correlation functions of fluctuations of the number of photons of interacting modes using a Monte–Carlo method. It is shown that in the stationary interaction limit, the value of these correlation functions strongly depends on the value of the coupling coefficient between the modes. It is shown that strong entanglement of the state of three interacting field modes is obtained in the case of weak coupling between the modes. In the case of extreme coupling between them, the value of the correlation function of fluctuations of the number of photons of the field modes tends to unity, because of which entanglement between the states of the modes disappears.