Coherent states and mode dynamics in Kerr nonlinear medium

Dynamics of three photonic modes in the theory of parametric amplifier in the medium, taking into account the Kerr nonlinearity, can be studied using the dynamical group WSp (6, R). For a degenerate parametric amplification with classical pump the description is reduced to the dynamics of coherent states of SU(1,1) group. The time dependence of average numbers of photons and squeezing are calculated. It is shown that the «switching-on» of the Kerr nonlinearity leads to suppression of the parametric amplification.