Entangled Field States in Terms of Quadrature Amplitudes in the Process of Nondegenerate Parametric Decay in an Optical Cavity

For the process of nondegenerate parametric decay in an optical cavity in which a photon with energy \(\hbar {{{{\omega }}}_{3}}\) decays into two photons with energies \(\hbar {{{{\omega }}}_{2}}\) and \(\hbar {{{{\omega }}}_{1}}\), where \(\hbar {{{{\omega }}}_{3}} = \hbar {{{{\omega }}}_{2}} + \hbar {{{{\omega }}}_{1}},\) the possibility of forming entangled field states of the interacting modes of the optical system based on the variable of quadrature amplitudes is studied. It is shown that strongly entangled states are obtained between the modes with the frequencies \({{{{\omega }}}_{2}}\) and \({{{{\omega }}}_{1}}\) in the case of a very strong coupling of the interacting modes. Weakly entangled states are formed in the case of strong coupling between modes, and no entanglement of these modes occurs in the case of weak coupling. In the optical system, the entangled states by the variable of quadrature amplitude do not form for the modes with frequencies \({{{{\omega }}}_{3}}\) and \({{{{\omega }}}_{1}}\).