The multimode even and odd coherent states (multimode Schrödinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of multivariable Hermite polynomials; the means and dispersions of the function are calculated. The conditions for the existence of squeezing are formulated. The correlations between the different modes of the Schrödinger cat states are studied. The transformation of the initial Schrödinger cat states under the action of a resonant external force is investigated.

• Received 21 October 1994

DOI:https://doi.org/10.1103/PhysRevA.51.3328