Assessing the Polarization of a Quantum Field from Stokes Fluctuations

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincaré sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.

Figure 1

(Top) Setup for efficient generation of a polarization squeezed state and the corresponding Stokes measurement apparatus. (Bottom) Measured variances for that state with the indicated scale (in dB noise power relative to the shot noise, marked by a white line). The minimum measured variance is $-5.0\pm 0.3\mathrm{dB}$. The white point in the $S_y$ axis is the tip of $⟨\widehat{\mathbf{S}}⟩$. We include also a zoom around the $S_x$ axis, near the minimum variance.

Figure 2

(Top) Setup for the generation of a squeezed vacuum in the horizontal mode and vacuum in the vertical one. We measure $-3.8\mathrm{dB}$ (8.6 dB) of quadrature squeezing (antisqueezing) in the horizontal mode. (Bottom) Measured variances $(\Delta S_{\mathbf{n}}{)}^2$ for the state as a color map on the Poincaré sphere with the indicated (linear) scale.