Experimental Violation of the Leggett-Garg Inequality Using the Polarization of Classical Light

In contrast to Bell's inequalities which test the correlations between multiple spatially separated systems, the Leggett-Garg inequalities test the temporal correlations between measurements of a single system. We experimentally demonstrate the violation of the Leggett-Garg inequality in a classical and macroscopic optical system using only the polarization degree-of-freedom of a laser beam. Our system is macroscopic due to the large number of particles involved and a laser beam is the closest experimental approximation to a coherent state, which is considered to be a classical state in the quantum optical sense. For a Gaussian beam under the paraxial approximation, the time evolution is equivalent to its propagation through space. The polarization of such a beam is measured with polarizing beamsplitters. The correlation functions can be obtained by placing the measurement devices at appropriate locations along the path. Our results show maximal violations of the Leggett-Garg inequality, which is evidence that classical wave mechanics is not a macrorealistic theory. The possibility of violating the Leggett-Garg inequality with the polarization of classical light comes from the superposition of temporally coherent fields.