State reduction for correlated photons in nonlinear optical process

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Abstract
Presents the study of the state reduction for correlated photons produced in a variety of optical processes such as parametric amplifiers, four wave mixers, down converters. The analysis includes losses in the system and is based on the general form of the Q-function and the Wigner function associated with correlated photons produced in the above optical processes. The author shows how the state of the a-mode can be obtained after he has carried a measurement on the b-mode. The measurement process itself has a simple interpretation in terms of the above quasi-probabilities. In the special case of parametric amplifiers without losses he recovers the results of Watanabe and Yamamoto, Phys. Rev., vol.A38, p.3556 (1988). His analysis is also applicable to the side modes generated by four wave mixing.