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.

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