Squeezing enhancement by competing nonlinearities: Almost perfect squeezing without instabilities

The competition between the ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ nonlinearity of a resonant second-harmonic-generation (SHG) system and an added ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ nonlinearity shifts the Hopf bifurcation of the standard SHG towards higher photon numbers eventually completely stabilizing the system. Remarkably, perfect squeezing survives the stabilization. Two important consequences are discussed, namely, efficient bright squeezing generation and strong suppression of the excess noise which, for parameters corresponding to an experiment reported in the literature, can be reduced by two orders of magnitude without diminishing the squeezing. Possible experimental implementations are finally discussed.