Polarization squeezing in a four-level system

We present a theoretical study of an ensemble of X-like 4-level atoms placed in an optical cavity driven by a linearly polarized field. We show that the self-rotation (SR) process leads to polarization switching (PS). Below the PS threshold, both the mean field mode and the orthogonal vacuum mode are squeezed. We provide a simple analysis of the phenomena responsible for the squeezing and trace the origin of vacuum squeezing not to SR, but to crossed Kerr effect induced by the mean field. Last, we show that this vacuum squeezing can be interpreted as polarization squeezing.