An optical Einstein-Podolsky-Rosen (EPR) state is produced in the spontaneous parametric down-conversion of an ultrashort classical pump pulse. It is shown both theoretically and experimentally that this results in the violation of a Bell-type inequality of the kind proposed by Grangier et al. The experiment is based on measuring interference between the light in the EPR state and weak light pulses in a coherent state. The maximum observed visibility of the interference pattern was $(89\mathrm{}\pm 4)\%.$ This interference can be regarded as a manifestation of nonlocality in the sense described by Banaszek and Wodkiewicz, even though the EPR state has a positive Wigner function. We develop the theory of two-channel homodyne detection with ultrafast pulses and then apply it to the EPR state generated in a type-II collinear geometry. Particular attention is paid to the investigation of how dispersion and phase matching influence the violation of local realism.

• Received 21 December 1999

DOI:https://doi.org/10.1103/PhysRevA.64.063804