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
EPR paradox, 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 1 model has been tested experimen-
tally 2 following a proposal of Croca, Garuccio, Lepore,
and Moreira 3. In the experiment Fig. 1 a 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 a repro-
duces single photon physics, b explains the observed vio-
lation of Bell-type experiments, c is consistent with the
results of the performed two-photon experiments, and d is
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