Almost perfect squeezing at high intensities by stabilization from competing non-linearities

The squeezing properties of a cavity Second Harmonic Generation (SHG) system with an added Kerr effect-like nonlinearity are studied as a function of the intra-cavity photon number. The competition between the second and the third order non-linearities shifts the Hopf bifurcation of the standard SHG towards higher intra-cavity energies eventually completely stabilizing the system. Remarkably, the noise suppression is at the same time strongly enhanced, so that almost perfect squeezing is obtained for arbitrarily large intra-cavity photon numbers. Possible experimental implementations are finally discussed.