Variance of a two-mode field under parametric excitation conditions

The quantum aspects of parametric excitation of two electromagnetic modes are considered. It is shown that a Gaussian wave packet, evolving in the two-dimensional space of these modes, is the exact solution of the Schroedinger equation. Equations are derived for describing evolution of the packet parameters with time. Perturbation theory is used to obtain explicit expressions for these parameters at low parametric excitation rates. It is found that the variance of the sum of the fields of these modes oscillates at the pump frequency. In contrast to parametric excitation of one mode, the minimum and maximum variance both increase with time. The increase in the minimum variance accounts for the small squeezing coefficients obtained experimentally for optical parametric oscillators. The effect is described by two squeezing coefficients.