Quantum versus stochastic or hidden-variable fluctuations in two-photon interference effects

Abstract

In a series of experiments performed by Mandel and co-workers, nonclassical effects have been demonstrated in the interference of two photons generated in a process of parametric down-conversion. The nonclassical effects in the two-photon interference effects can be discussed in the framework of two different descriptions. In the first description, a stochastic theory of electromagnetic field fluctuations can be used in order to calculate the interference pattern. In the second description, a theory of hidden-variable fluctuations can be applied in order to calculate correlations of the interference pattern. A stochastic theory leads to statistical inequalities for the light intensities, while a local hidden-variable theory leads to Bell’s inequalities. Using the Schwinger-boson representation of the angular momentum, we show that the two-photon interference effects can be described in terms of spin-correlated states. In particular, we show that the action of a beam splitter on the photons in a parametric down-conversion is equivalent to the production of an entangled state that is very similar to the well-known Einstein, Podolsky, and Rosen spin-singlet state. We show that the stochastic theory of two-photon fluctuations is not equivalent to a hidden-variable theory of photon correlations. We establish a range for which the stochastic theory fails but the hidden-variable theory is still possible. We compare our theoretical predictions with the experimental results and conclude that a violation of the stochastic theory has been clearly observed, while the violation of the hidden-variable theory is less pronounced.