EFFECT OF THE PUMP STATE ON THE DYNAMICS OF THE PARAMETRIC-AMPLIFIER

The parametric amplifier is usually studied under the assumption that the pump mode is in a large-amplitude coherent state. We consider what happens when this is no longer the case. We first derive some exact r elations between the number fluctuations of the pump and signal, the p ump and the idler, and also the signal and the idler. It is then deter mined how much phase noise can be tolerated in the initial pump state if two-mode squeezing is to be produced in the signal-idler field. The relation between the rotational symmetry in phase space of the initia l pump state and that of the signal-idler subsystem is determined. We find that the Sum phase distribution of the signal and idler has twice the rotational symmetry as that of the initial pump state. Finally, w e generalize the parametric approximation to treat pump states which a re not coherent states. We examine the effect of a phase-squeezed pump state and find that the pump squeezing can actually decrease the two- mode squeezing of the signal-idler field while enhancing a form of hig her-order squeezing, sum squeezing, for these fields.