Experimental Bell violations with classical, non-entangled optical fields

We report experiments in which the Bell parameter S that enters the Clauser-Horne-Shimony-Holt inequality: |S| ≤ 2, attains values |S| < 2. In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η(α,β). This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β, which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S. By changing the amount of field correlation, we could cover a range that goes from |S| < 2 to |S| > 2. Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum-classical border.