On the squeezing obtainable in parametric oscillators and bistable absorption

We show that the maximum reduction of fluctuations that can be obtained in a degenerate parametric amplifier at steady state is by a factor of two, whatever is the ratio between the damping states γ ₁ and γ ₁ of the two modes which interact in the cavity. Thus, we generalise the recent results of Milburn and Walls, derived in the limit γ ₂ ≫ γ ₁. We give simple analytic formulas for the fluctuations. In the case of absorptive optical bistability we find a small squeezing effect in the amplitude of the transmitted field in part of the low transmission branch.