We predict the generation of noncritically squeezed light through the spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model considers a χ (3) cavity that is pumped by two Gaussian beams of frequencies ω1 and ω2. The cavity configuration is such that two signal modes of equal frequency ωs = (ω1 + ω2) /2 are generated, these signal fields being first order Laguerre-Gauss modes. In this system a spontaneous breaking of the rotational symmetry occurs as the signal field corresponds to a Hermite-Gauss TEM mode. This symmetry breaking leads to the perfect and non-critical (i.e., non dependent on the parameter values) squeezing of the angular momentum of the output TEM mode, which is another TEM mode spatially orthogonal to that in which bright emission occurs.Index Terms-quantum fluctuations, four-wave mixing, nonlinear optics, squeezed light.

We discuss the possibility of generating noncritical quadrature squeezing by spontaneous polarization symmetry breaking. We first consider Type II frequency-degenerate optical parametric oscillators but discard them for a number of reasons. Then we propose a four-wave-mixing cavity, in which the polarization of the output mode is always linear but has an arbitrary orientation. We show that in such a cavity, complete noise suppression in a quadrature of the output field occurs, irrespective of the parameter values.

We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic χ (3) medium in which self-phase and cross-phase modulation, as well as four-wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the orthogonally polarized vacuum mode, and show how this produces polarization squeezing.

It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s-ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s-ordered quasiprobability distribution verifies a true Fokker-Planck equation, i.e., the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s-ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.

In the last years we have proposed the use of the mechanism of spontaneous symmetry breaking with the purpose of generating perfect quadrature squeezing. Here we review previous work dealing with spatial (translational and rotational) symmetries, both on optical parametric oscillators and four-wave mixing cavities, as well as present new results. We then extend the phenomenon to the polarization state of the signal field, hence introducing spontaneous polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in which the phenomenon can be investigated at the singlephoton-pair level in a non-dissipative case, with the purpose of understanding it from a most fundamental point of view. I TRODUCTIO MotivationNon-classical states of light have been a subject of active research in the last decades. Squeezed states are probably one of the most simple examples of them: in contrast to the coherent states (like the usual laser light or the vacuum), where both quadratures of light have the same uncertainty, in an ideal squeezed state quantum fluctuations are reordered such as one of the quadratures is free from noise, while the other is completely undetermined 1 .Soon after the concept of squeezed light was introduced, it was proved that nonlinear resonators were able to generate it 1 . In particular, it was shown that both degenerate optical parametric oscillators (DOPOs) and degenerate four-wave mixing cavities −which are, respectively, optical resonators with a χ (2) nonlinear crystal and a χ (3) nonlinear medium inside−, were able to create a highly squeezed vacuum in the output field at the degenerate frequency (signal frequency in the following) when working close to their emission threshold. However, DOPOs operated below threshold are nowadays the most common source for squeezed light, most of all because χ (3) media are usually affected by residual processes that provide extra noise (such as spontaneous emission or different types of scattering). Although noise reduction cannot be complete, as this would entail infinite fluctuations in the anti-squeezed quadrature (which requires infinite energy), squeezing levels as large as 11.5 dB (more than 90% of noise reduction) have been proved 2 . On the other hand, the squeezing level attained at threshold degrades as the system is brought apart from it, and hence this squeezing is critical as it requires a tuning of the system parameters.Squeezed light has found major applications in several fields like high precision measurements 3,4 and quantum information 5 , a reason why it is important to keep improving its quality and finding new sources able to generate it. This was the main motivation that led us to propose the study of the phenomenon of spontaneous symmetry breaking (SSB) in nonlinear cavities as a potential resource for squeezing.