Quantum Fluctuations in the Stokes Parameters of Light Propagating in a Kerr Medium with Dissipation

Exact analytical expressions describing the evolution of the expectation values and the variances of the Stokes operators are derived for the elliptically polarized light propagating in a Kerr medium with dissipation. It is shown that quantum fluctuations of the field essentially affect the polarization of the field. The explicit quantum formulas describing the azimuth and the ellipticity of the polarization ellipse as well as the degree of polarization are derived and illustrated graphically. Quantum fluctuations in the Stokes parameters are discussed, and the evolution of the signal-to-noise ratio is shown to be reduced by the quantum field fluctuations. Role of the dissipation is shown explicitly in a fully quantitative way from the exact analytical solutions.