  We study the interaction of a nearly resonant linearly polarized laser beam
with a cloud of cold cesium atoms in a high finesse optical cavity. We show
theoretically and experimentally that the cross-Kerr effect due to the
saturation of the optical transition produces quadrature squeezing on both the
mean field and the orthogonally polarized vacuum mode. An interpretation of
this vacuum squeezing as polarization squeezing is given and a method for
measuring quantum Stokes parameters for weak beams via a local oscillator is
developed.
