Squeezing resulting from a fourth-order interaction in a degenerate parametric amplifier with absorption losses

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Abstract
The squeezing properties of a model of a degenerate parametric amplifier with absorption losses and an added fourth-order nonlinearity have been analyzed. The approach used consists of obtaining the Langevin equation for the optical field from the Heisenberg equation provided that a linearization procedure is valid. The steady states of the deterministic equations have been obtained and their local stability has been analyzed. The stationary covariance matrix has been calculated below and above threshold. Below threshold, a squeezed vacuum state is obtained and the nonlinear effects in the fluctuations have been taken into account by a Gaussian decoupling. In the case above threshold, a phase-squeezed coherent state is obtained and numerical simulations allowed to compute the time interval, depending on the loss parameter, on which the system jumps from one stable state to the other. Finally, the variances numerically determined have been compared with those obtained from the linearized theory and the limits of validity of the linear theory have been analyzed. It has become clear that the nonlinear contribution may perhaps be profitably used for the construction of above-threshold squeezing devices.