EFFECT OF THE PUMP STATE ON THE BEHAVIOR OF THE DEGENERATE PARAMETRIC-AMPLIFIER

We study the effect of non-coherent-state pumps on the behavior of the degenerate parametric amplifier. This is done both by developing some exact results and by extending the parametric approximation. Relation s are found between the number fluctuations in the pump and those in t he signal. The effect of initial phase uncertainty in the pump on the squeezing in the signal is also determined. In addition, we find that rotational symmetry in phase space of the signal-mode state is twice t hat of the pump-mode state. This implies, for example, that a pump in the squeezed vacuum state will produce a signal-mode state with a four -pronged structure. The effect of a squeezed pump with nonzero amplitu de is studied by using a more general form of the parametric approxima tion. It is shown that in the time interval during which the parametri c approximation is valid the effect of this pump is the same as one wh ich is an incoherent superposition of coherent states. We find that wh ile the squeezing of the pump degrades the squeezing of the signal it enhances its amplitude-squared squeezing.