Volume 90A, number 1,2 PHYSICS LETTERS 21June1982

NEW EXPERIMENTAL SET-UP FOR THE DETECTION OF DE BROGLIE WAVES *

August0 GARUCCIO Istituto di Fisica dell’Universit& INFN, Sezione di Bari, V. Amendola 173, 70126 Bari, Italy

Vittorio RAPISARDA Istituto di Fisica dell’Universit~, INFN, Sezione di Catania, C. ItaIia 57,95129 Catania, Italy

Jean-Pierre VIGIER Labomtoire de Physique Thbrique, ERA. no. 533 associie au CNRS, Institut H. Poincar& II Rue P. et hf. Curie, 75231 Patis Cedex 05, France

Received 14 October 1981 Revised manuscript received 19 April 1982

We present a new experimental set-up to detect the existence of de BrogIie waves. Since it uses only one, very weakened, incoherent source it escapes preceding objections and can test conflicting predictions of the Copenhagen (CIQM) and causal stochastic (SIQM) interpretation of qunatum mechanics.

In order to detect the possible real physical exis- tence of de Broglie waves, Garuccio and Vlgler [l] fol- lowed by Garuccio, Popper and Vigler [2] have dis- cussed an experimental set-up devised (i) to produce testable conflicting predictions of the causal stochas- tic (SIQM) [3] and Copenhagen (CIQM) lnterpreta- tions of quantum mechanics; (ii) to test a new para- dox suggested by Popper [2,4].

This proposal, based upon a modified version of the Pfleegor-Mandel experiment, has provoked a com- plex and heated discussion [S-7]. Besides its experi- mental difficulty (it is delicate to correlate the phases of two separate laser beams), its feasibility has been essentially contested on the basis of the laser nature of the source.

In fact the existence of a Poisson distribution of photons in laser beams has been used [6,7] to justify the point that no testable difference exists between the consequences of both interpretations.

The aim of the present letter is to present an ex- perimental programme and experimental set-up which clearly falls outside the field of the above men-

* Work supported by INFN, MPI, CNR and CNRS. For footnote see next page.

tioned objections to the preceding discussion and sup- presses, as far as possible, experimental difficulties This set-up is described in fig. 1.

A single very weakened pulsed source (i.e. a lm- pulsed led) produces, one by one, independent wave packets, which contain single photons at the same frequency.

These successive wave packets containing 1 photon only, denoted IW,‘(n = 1,2, . ..). are split by a semi- transparent beam splitter (the semi-transparent mirror Ml with a transrnlssion coefficient l/2) and one knows from CIQM that the photons pass, one by one, either in the reflected packets RW, or in the transmitted packets TW, with a probability l/2; there is a 100% anticorrelation between reflected and transmitted pho- tons, as has been recently verified experimentally by Mandel et al. [8].

Followlng a suggestion of Selleri [9], we then lntro- duce along the path of TW, an organic laser gain tube (LGT) which multiplies the photon number by two (on the average) and preserves the different phases of TW, *I. This is perfectly feasible. As one knows, gain

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Volume 90A, number 1,2 PHYSICS LETTERS 21June1982

tubes amplify externally introduced photons beams and preserve their phases with sharp temporal correla- tion, so that one can expect this to hold in the one photon limit also. Such amplifiers have been used re- cently (as will be discussed presently) in a different context by Martinolli [lo] in Prof. Gozzini’s labora- tory in Pisa to test for the two photons incoming case the outgoing distribution generated by a semi-transpa- rent mirror.

Of course the use of this multiplying gain tube im- plies a preliminary test, i.e. one should test if in the setup of fig. 2, where incoming isolated photon beams

*I The question of the phase conservation between the phases of separated incoming wave packets and the corre- sponding outgoing photon pairs, theoretically valid be- cause of the laser character of LGT should be tested sep- arately by verifying that the set-up of fii. 1 maintains an interference pattern at ordinary light intensity.

Fig. 1.

1

are split by M, , there are significant anticoincidences (= 100%) between photomultipliers PM, and PM, de- tecting photons in RW and TW. Indeed, as pointed out by Selleri [9] if there are less anticoincidences, then the photon empty TW de Broglie wave packet would excite, without photons, the LGT and, contrary to CIQM predictions, induce a real physical effect.

If anticoincidences between PM, and PM2 persist, then one can move a step further since only a photon in TW can induce two photon wave packets in LGT, which are split in their turn by a beam splitter M2 identical to M, .

At this stage we are back to the experimental set- up of Martinolli and Gozzini[ lo], i.e. we have the si- tuation of fig. 3, where the beam splitter M2 intro- duces three independent situations i.e. the cases (a), (b), (c) described in fig. 4.

There are conflicting views in the literature [2,10]

Fig. 2. Fig. 3.

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Volume 90A, number 1,2 PHYSICS LETTERS 21 June 1982

4 b)

Fig. 4.

on the action of M2 on a two photon beam. On the basis of the idea that photons behave independently in the incoming wave packet and that each photon has an independent probability l/2 of going in RW or in TW, many people (including two authors of this letter [2]) were tempted to write that, with the incoming probability P(2) = 1, one has Pa = Pb = l/4 and PC = l/2. This erroneous view disagrees both with Bose- Einstein statistics and experiment. Indeed from this Statistics’Dirac [ 1 l] has deduced Pa = Pb = PC = l/3, a result which shows that photons are not independent in Bose-Einstein statistics.

Moreover the Martinolli-Gozzini experiment [lo] strongly suggests the l/3 value. Indeed the prediction P, =Pb = 1/4,P, = l/2 suggests in their sample the predicted theoretical value of 1600 -+ 600 correlations, while experiment yields 1070 + 30, i.e. compatible with prediction P, = Pb = PC = l/3.

If further tests confirm this, then one sees that the LGT outgoing photons have a l/3 probability of pro- ducing coincidences between the photomultiplier PM, and the interference region (IR), where a detec- tor devised by Mandel and Pfleegor [ 121 is built with a stack of thin glass plates (see inset of fig. 1) each of which has a thickness corresponding to a half fringe width. The plates are cut and arranged so that any photons falling on the odd plates are fed to one pho- tomultiplier mA, while photons falling on the even plate are fed to the other PM,. So the LGT outgoing photons have a l/3 probability of producing coinci- dence between PM, and one of two photonmulti- pliers PMA or PM,.

The experiment is now to analyze the rate of ob- serve coincidences between PM,, PMA and PM,. Two perfectely conflicting results are now theoretically pos- sible:

(A) According to CIQM no interferences should be observed, i.e. the rate of observed coincidences should be equal to 1. Indeed if 2 photons appear at Pq, no photons should appear at I%!A or PM,. Morover if

one photon appears at pMc and one in PM, or PM,, then since one now knows that no photons have taken the Ml -M,-IR path, then no interference should ap- pear. Indeed the passage of a photon in the LGT path has collapsed the RW packet.

(B) According to Maxwell’s theory of light (or the SIQM) [3] interference fringes should appear with the maximum contrast, i.e. the rate of observed coin- cidences should be different from 1, since one has Z(RW) = Z(‘IW”) = Z/2. Indeed even if the incoming photons of IW have entered the LGT, then a real physical de Broglie wave is moving with RW along the path M, -M,-IR. This induces a stable interference pattern since the path difference between Ml-MS--IR and M, -LGT-M2-M,-M,--IR is constabt.

As one can easily check, these predictions escape all preceding objections. If LGT (according to CIQM) needs real incoming photons to be excited, then no photon in our coincidence scheme can travel along the M, -M,-IR path, so that the detection of inter- ferences (according to SIQM or Maxwell’s theory) would really constitute a crucial contradiction between CIQM and reality.

References

[l] A. Garuccio and J.P. Vigier, Found. Phys. 10 (1980) 791.

[2] A. Garuccio, K. Popper and J.P. Vigier, Phys. Lett. 86A (1981) 397.

[ 31 For references see: J.P. Vigier, Lett. Nuovo Cimento 24 (1979) 258,265; 29 (1980) 467.

[4] K. Popper, private communication. [S] W.M. de Mynch, Epist. Lett. 28 (1980) 33;

B. Hiley, private communication. [ 6 ] J. Andrade de Silva and A. Andrade de Silva, Epist.

Lett. 29 (1980) 39. [ 71 0. Costa de Beauregard, Epist. Lett. 28 (1980) 7; 30

(1980) 30. [8] L. Mandel and K. Dajenais, Phys. Rev. Lett. Al8 (1978)

2217. [ 91 F. Selleri, Can an actual existence be guaranteed to

quantum waves?, to be published. [lo] R. MartinoBi (relatore A. Gozzini), Un esperimento di

ottica a mtensiti molto basse, Tesi di Laurea, Universiti di Piss (1980).

[ll] P.A.M. Dirac, I principi della mecca&a quantistica (Boringhieri, Torino, 1976) p. 291; see also RP. Feynman, The Feynman lectures on phy- sics (Int. Eur. Edit., Amsterdam, 1975) Ch. 4.

[12] R.L. Pleegor and L. Mandel, Phys. Rev. 159 (1967) 1084.

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