Down-conversion Photon Pairs: A New Chapter In the History of Quantum Mechanical Entanglement

An entangled state of a many-particle system is one which cannot be expressed as a product of single-particle states. We summarize the major steps  in the history of this concept, notably Schrodinger's original recognition of entanglement, its role in the Gedankenexperiment of Einstein-Podolsky-Rosen, and the Bohm-Aharonov demonstration that photon pairs from positronium annihilation are entangled. We then show that interferometric phenomena of photon pairs generated in parametric down-conversion are manifestations of entanglement, and we analyze two experiments in which different types of entanglement appear: that of Ghosh and Mandel, in which there is entanglement of directions of wave-vectors, and that of Kwiat et al., in which there is entanglement of magnitudes of wave-vectors (or wave-numbers).