We perform an optical beam splitting experiment, using a light field, in which the photons arrive in pairs. It is proven that the distribution of photons in the reflected and transmitted beam obeys a binomial distribution.
The probability of separating k particles from a beam of n classical distinguishable particles by a beam splitter is given by the Bernoulli distribution. When turning to indistinguishable Bose quantum particles, this distribution is preserved by a refined interplay between interference and stimulation effects. This behaviour is demonstrated in an experiment where pairs of photons interact with an optical beam splitter. The distinguishability of the photons within a pair is changed by varying the degree of coherence.
We investigated statistical fluctuations in the numbers of photons contained in the correlated twin photon beams generated by an optical parametric process. The coincidence between the signal- and idler-photoelectron pulses from a pair of avalanche photo-diodes was measured. The measured fluctuation in the number of signal-photons coinciding with idler-photons was equal to the standard deviation of a binomial distribution and was smaller than that of a Poisson distribution. We determined that even when the quantum efficiency of the photon detectors was much lower than unity, the uncertainty in the number of photons obtained with the twin photon beams was smaller, by a factor of 1/√2, than that with a classical light beam.
This work proposes to investigate the photon statistics of the light transmitted and reflected by a two-dimensional array of interacting atoms. The reflected beam is characterized by photon antibunching. On the other hand, in the transmitted beam the indistinguishability between the driving laser photons and the photons reemitted by the atoms results in photon bunching. The overlap between the driving and scattered fields is enhanced by the cooperative optical response of the atomic array. In the examples used in this paper, up to 25% of the transmitted photons are grouped in pairs. The simulations are carried out using the stochastic method of quantum trajectories.