Experimental characterization of the Gaussian state of squeezed light obtained via single-passage through an atomic vapor

We show that the description of light in terms of Stokes operators in combination with the assumption of Gaussian statistics results in a dramatic simplification of the experimental study of fluctuations in the light transmitted through an atomic vapor: no local oscillator is required, the detected quadrature is easily selected by a wave-plate angle and the complete noise ellipsis reconstruction is obtained via matrix diagonalization. We provide empirical support for the assumption of Gaussian statistics in quasi-resonant light transmitted through an $^{87}$Rb vapor cell and we illustrate the suggested approach by studying the evolution of the fluctuation ellipsis as a function of laser detuning. Applying the method to two light beams obtained by parting squeezed light in a beamsplitter, we have measured entanglement and quantum discord.