ARTICLES Experimental test of Selleri’s variable photodetection-probability model A. Garuccio, * J. R. Torgerson, C. Monken, D. Branning, and L. Mandel Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 Received 27 October 1995 Selleri’s model of photodetection based on variable detection probability is analyzed. The results of an experiment that discriminates between the predictions of Selleri’s model and quantum mechanics are presented Bell’s Theorem and the Foundations of Modern Physics, edited by A. van der Merwe, F. Selleri, and G. Tarozzi World Scientific, Singapore, 1992; in Wave-Particle Duality, edited by F. Selleri Plenum, New York, 1992. PACS numbers: 03.65.Bz In recent years several experiments have been performed to test the validity of de Broglie’s and Einstein’s ideas on the foundations of quantum mechanics. Most of these were based on coincidence detection of photon pairs in different branches of a particular experimental setup, for which the predictions of quantum mechanics and the de Broglie theory or Einstein locality are in conflict. Correlated photons emit- ted in an atomic cascade were used in the first of these ex- periments, but in recent years the photons were produced in the parametric down-conversion process instead. With this source, some interesting experiments have been performed in order to test quantum optics, the Einstein-Podolsky-Rosen EPRparadox, semiclassical radiation theory, and de Bro- glie’s empty wave theory. In particular, the reality of the wave associated with each photon in de Broglie’s 1model has been tested experimen- tally 2following a proposal of Croca, Garuccio, Lepore, and Moreira 3. In the experiment Fig. 1a parametric down-converter pumped by uv laser light produces pairs of linearly polarized photons. The two photons are generated simultaneously, and following different paths, form two beams, the signal and idler beams. The beams pass through a modified Mach-Zehnder interferometer with three semitrans- mitting mirrors, and the optical path length is varied by mov- ing the mirror Q . The experiment consists of counting the events in which the idler photon, after traversing BS 3 and BS 1 , is detected by the photomultiplier D 1 , and the signal photon is detected simultaneously by the photomultiplier D 2 after passing BS 1 and BS 2 . The measured coincidence counting rate is proportional to the joint-detection probability for D 1 and D 2 . If we assume the reality of de Broglie’s wave, this joint detection probability should exhibit modula- tion as a function of the optical path difference between the two paths P -R -U -D 1 and P -Q -U -D 1 , while quantum me- chanics predicts a probability independent of these optical lengths. The difference is due to the fact that at U there is an overlap of the idler wave with the empty wave generated by the signal photon passing BS 1 and BS 2 . The results of the experiment are in agreement with quantum mechanical pre- dictions and contradict what is expected on the basis of the de Broglie pilot wave theory. A different interpretation of these results has been pro- posed by Selleri 4,5, based on the idea of a variable detec- tion probability for the photodetectors. From a realistic and causal point of view, it is possible to develop variable prob- ability detection models that divide the set S of detected objects into a number of subsets S i with probabilities P i to be detected, so that the overall detection probability is the average over i , P =P i . These models agree with quantum mechanics for the single channel counting rates. However, since the average of a product is in general different from the product of the averages, it is in two-particle detections that one might expect a departure from de Broglie’s assumption about the detection probability. In particular, the model discussed by Selleri arepro- duces single photon physics, bexplains the observed vio- lation of Bell-type experiments, cis consistent with the results of the performed two-photon experiments, and dis compatible, within experimental errors, with the Wang, Zou, and Mandel experiment 2. It has been shown that a simple experiment can test * Permanent address: Dipartimento di Fisica, Universita ` di Bari, INFN-Sezione di Bari, Via Amendola 173, 70126 Bari, Italy. FIG. 1. The Wang-Zou-Mandel experimental setup. The align- ment is critical because it is necessary to ensure the spatial super- position at BS 1 of the empty wave and of the full wave associated with the idler photon. PHYSICAL REVIEW A MAY 1996 VOLUME 53, NUMBER 5 53 1050-2947/96/535/29444/$10.00 2944 © 1996 The American Physical Society