Quantum correlations close to a square pattern forming instability

Quantum fluctuations and correlations at the onset of the instability that leads a square pattern in a degenerate optical parametric oscillators OPO are studied. Using a full nonlinear model, anticorrelation is found to be present above or below threshold. Above threshold, this anti- correlation comes from linear coupling in the linearized equations. Below threshold, it is a manifestation of non-linear critical fluctuations, and therefore it can be observed only very close to threshold.