Bell Experiment with Classical Optical Fields

We theoretically and experimentally explore the implications of entanglement in statistically classical optical fields \footnote{X.-F. Qian, Bethany Little, John Howell, and J. H. Eberly, Optica {\bf 2}, 611-615 (2015).}. The description of these fields in terms of polarization and amplitude degrees of freedom can take a non-separable form which employs a mathematical description of entanglement often associated with quantum phenomena. By subjecting these optical fields to a Bell analysis, we examine the role of entanglement in marking the quantum-classical boundary. We report a value of the Bell parameter greater than $\cal B$ $ = 2.54$, many standard deviations outside the limit $\cal B$ $ = 2$ established by the Clauser-Horne-Shimony-Holt Bell inequality \footnote{John F. Clauser, Michael A. Horne, Abner Shimony, and Richard Holt. Phys. Rev. Lett. {\bf 23}, 880-884 (1969)}. This suggests that Bell violation has less to do with quantum theory than previously thought, but everything to do with entanglement.