Optical Wigner functions for two-photon entangled wave packets

Einstein-Podolsky-Rosen (EPR) correlations produced for two-photon entangle d wave packets are analyzed by use of optical Wigner functions. In particul ar, type-II optical parametric downconversion systems are used, and the eff ects of the length of the crystal and the filter bandwidth on the Wigner fu nctions are studied. The relation between the optical Wigner functions and the interference experiment with a beam splitter is studied. We find that, whereas in first-order correlation experiments (typified, for example, by Y oung's interference experiment) the "photon interferes with itself" [P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon, Oxford, UK, 1958) , p. 9], in the EPR correlations the two-photon amplitude function interfer es with itself. Such interference is analyzed by use of the optical Wigner functions. (C) 1999 Optical Society of America [S0740-3224(99)01610-0].