Abstract

The use of parametric down-conversion as a convenient source of correlated photon pairs dates back to the early 1970's but it was not until the late 1980's and early 1990's that these sources were shown to be useful for fundamental studies of the phenomenon of two particle entanglement [1]. In recent experiments three photon interference effects have been studied by entangling initially separate photons [2] which has led on to demonstration of quantum teleportation and three photon entanglement via GHZ states. Due to the necessity for overlapping weak beams of randomly timed photon pairs the triple coincidence rates in these experiments is low. Furthermore the three-photon interference effects are post-selected from a product state of two-photon entanglements which opens the experiments to criticism from a local realistic viewpoint. An improved source would create entangled states of three photons directly in a way analagous to two-photon downconversion. This work extends the quantum theory of spontaneous two-photon downconversion in the presence of a χ⁽²⁾ non-linearity to the three photon case based on the non-linear susceptibility χ⁽³⁾. The resulting gain is much lower and the efficiency for the three-photon creation process is small. However we show by simple arguments that the number of modes scale quadratically with bandwidth. This leaves us with the hope of detecting of order one three photon per second when phase matching allows a 10nm bandwidth.

© 2000 IEEE