Quantum physics for correlated photons

Vistas/nAstronomy,Vol.37,pp.217-220, 1993 Printedin C-r~tBritain.All rightsr-,,erntl.

0083--6656/93 $24.00 © 1993 P~gmnon Press Ltd

QUANTUM PHYSICS FOR CORRELATED PHOTONS Augusto Garuccio Dipartimento di Fisica dell'Universit,~, INFN - Sezione di Bad, Via Amendola 173, Bad, Italy

INTRODUCTION Photon pairs are ideal tools for testing new and anomalous features of Quantum Physics. Correlated photons emitted in an atomic cascade have been used in most of the performed experiments testing Quantum Mechanics versus Local Realistic Theories via Bell's inequality. Moreover in the recent years the parametric-down conversion process has been used in order to produce pairs of identical photons. Using this pairs, many interesting and surprising experiments have been performed on Quantum Optics, on EPR paradox and on Semiclassical Theory of Radiation. Recently, L.J. Wang, X.Y. Zou and L. Mandel(1990), following a proposal made by J.R. Croca, A. Garuccio, V.L. Lepore and R.N. Moreira(1990), have carded out an experiment for testing the de Broglie theory of pilot wave using this source of photon couples. This recent experiment is the first direct test of the de Broglie's assumption of the existence of a real wave propagating in space and time and the negative result of the experiment puts serious problems to the de Broglie guided-wave theory. The compatibility between the de Broglie theory and the recent experiments using photon pairs emitted in parametric-down conversion process will be analysed in this contribution and new experimental test on foundations of quantum mechanics will be presented and discussed. THE DE BROGLIE THEORY From Bell's inequality we know now that any local and causal theory is incompatible with quantum mechanics; more precisely not all the results of quantum mechanics can be reproduced in a local realistic theory. Then - in principle - it is possible to find experiments that lead to conflicting testable predictions of quantum mechanics and the de Broglie pilot wave theory. In particular, the problem concerning the reality of de Broglie waves has been discussed recently in several experimental proposals.Essentially the question is related to the "correct" interpretation of the wave function ~F whether it must be interpreted as a simple tool for predicting mathematical probabilities or, on the contrary, whether it represents, as suggested by de Broglie, a real physical wave propagating in spacetime. Let us state explicitly the basic assumptions within the de Broglie model: (1) A photon is composed of a localised particle and a real wave dp propagating in space and time in accordance with d'Alambert equation..

As because of this assumption, when a photon impinges on a semitransmitting mirror, the associated wave is partly transmitted and partly reflected, while the particle is either transmitted or reflected. Obviously, the detection of the particle in one of two channels does not induce the collaose of the real

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wave in the other channel. For example, speaking about the theory of double solution, de Broglie(1968) wrote:

This solution involves the existence of two different waves, one of which is objective and represents a physical reality which, because is intimately linked with the particle, enables its behaviour to be determined. The other is a subjective construction, which is based on the information which we posses about the objective wave and provides us with a probability representation for the particle. (2) I f in a region o f space, n waves eP1, eP2 . . . . .

0 n are present, the total wave is given by the sum

We stress that the previous assumption holds even when the waves come from different sources, as in the famous Pfleegor and Mandel (1967) experiment, de Broglie and Andrade e Silva(1968), commenting on the results of the experiment, wrote: A photon coming from one laser or the other and arriving in the interference zone is guided, and this seems us physically certain, by the superposition of the wave emitted by the two lasers" and "The movements of the photon in the interference zone are actually guided by that superposition, and not by the single wave that carried it. (3) "In an interference field, the probability of a photon's being present at a given point is ... proportional to the square o f the amplitude o f the wave present at that point. [de Broglie and Andrade e Silva(1968)] THE EXPERIMENTAL PROPOSAL Now, recent interference of two identical photons produced in parametric down conversion have opened the way to clarify the problem of reality of empty wave [Croca, J.R., Garuccio, A., Lepore, V.L. and R.N. Moreira, (1990)]. A parametric-down converter (pumped by U.V. laser light) produced pairs of linearly polarised photons; the two photons are generated simultaneously and, following different paths, form two beams, the signal and the idler beams. The beams go through a modified Mach-Zhender interferometer (Fig. 1) in which all the mirrors are semitransmitting and the optical lengths can be varied by a phase-shifter PS. We will consider the events in which the idler photon, after traversing BS 1 and BS4, is detected by the photomultiplier D 2, and the signal photon is detected by the photomultiplier D 1 after traversing BS z and BS 3. The measuring quantity is the joint-detection probability in D 1 and D 2 as a function of the optical length difference between the two paths BSI-BS4-BS3 and B S F B S r B S 3 . Two perfectly conflicting results are now theoretically possible: According to quantum mechanics no interference should be observed (i.e., the rate of coincidence D 1D 2 is constant). Indeed if two photons appear at D 1 , no photon should appear in D2 , moreover if one photon appears at D~ and one appears in D 2 then we know that no photons have taken the BS4-BS 3 path and we axe sure that no interference should appear. The detection of the idler photon in D z has collapsed the wave packet. -

- According to de Broglie model an interference pattern should appear. Indeed, even if the idler photon is detected in D2 , then a real physical de Broglie wave is moving along the path BS4-BS3 and overlaps in BS 3 with two waves: the (coherent) empty wave produced from idler photon in BS 1 and travelling along the path BSI-BS2-BS3 ; the (incoherent) signal photon carrying wave travelling along the path BS2-BS3 .

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Quantum Physicsfor Correlated Photons

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Fig. 1. The Croca, Garuccio, Lepore, Moreira experimental set-up. More precisely, introducing the usual transmission and reflection coefficients t and r satisfying the relations Irt2 + It]2 = 1, and rt* + r*t = 0, the outgoing waves can be written, using the assumption (2) of the de Broglie theory, as ~1 = t201 + r2t02 + ta202 eiS,

~t2 = t24)2 e i5.

Since • 1 and 4~2 have random phase, the coincidence probability between D 1 and D 1 is P(D1,D 2) = ohazld2[ItlnIOll2 + 21r141t121OJ2(1 + cosS)], where P(DI,D2) depends upon the phase difference between the two optical lengths of the interferometer. In quantum optics the joint probability is PQM(D1,D2) = C(Itl2) 4. This experiment has been performed by Wang, Zou, and Mandel (1991). The crucial point of the experiment is the overlapping of signal (full) wave packet with the empty wave packet on the beamsplitter BS2.and this was checked from the Authors with a particular coincidence technique.As is known, the results of the experiment agree with quantum mechanical predictions and contradict what is expected on the basis of the de Broglie theory. A first criticism to this experiment was based on the position of filters - before the photodetectors and not before the apparatus [Croca, Garuccio, Lepore, Moreira, (1992)]. The real coherence length of the wave packets inside the interferometer is 10 time shorter than the coherence length determined by the filters; then the calibration of the photon paths based on this large coherence length does not assure that the packets are superimposed in BS 2 and that in the same region of space two real waves overlap. A new version of the experiment was performed by Wang, Zou, Mandel, (1992) following the previous remarks and the results are essentially the same as before. A different criticism of the results has been proposed by SeUeri (1992) and it is based on variable photon detection probability. Starting from a realistic and causal point of view it is possible to develop variable probability detection models (VDPM) that split the set S of detected objects in a certain number of subsets S i with probability Pi to be detected so that the overall detection probability results from the average of different probabilities P = i.These models agree with q.m. for single photon detection probability, but, since the average of a product is in general different from the product of the averagee, it ~s m the case of two-partice observations that one can expect departure both from the q.m. and de Broglie's third assumption on detection probability. In particular, the model discussed by Selleri a) reproduces single photon physics; b) explains the observed violation of Bell'type experiment; c) is consistent with the results of the performed two-photon experiments; d) is compatible, within the experimental errors, with the Wang, Zou, and Mandel (1991) experiment.

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We will present now an easy experimental configuration which can test this model with respect q.m.. Let us consider a photon pair produced in a parametric down-converter (Fig, 2); the two photons have the same linear polarization, v.z. along z-axis, and travel in x-y plane. The signal and idler beams impinge on two linear polarizers oriented along the same direction making an angle 0 with z-axis. The two polarizers can rotate of the same angle and mantain everiday the same direction. Two photomultipliers 1 and 2 detect the photons passed through the polarizators; the outputs of photomultipliers are collected in two counters C 1 and C 2 and in a coincidence circuit Ct2. The measured quantity is the ratio R between the probability over the product of the probabilities of the single detection as a function of the angle 0 of both polarizers. o

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Fig. 2. The proposed experimental set-up for testing variable detection probability. In the Selleri's model the detection probability depends on a new variable la which, for semplicity, is assumed equal +1 or - l a n d equiprobable and on amplitude of wave function and it is given by D(kt) = 1][1+ I.trl(1-rl)(1-2 IVI21 where 1] is the (average) measured quantum efficiency of photomultiplier. It is easy to see that, using the previous formula, averaging over I.t and assuming that the Malus low holds for the transmission probability of polarizeres, the probability of single photon detection is P(1) = P(2) - rl cos 2 0. whereas the joint probability detection of two photons resultsP(1,2) = rl2cos 4 0[ 1+ (1-rl) 2 cos 2 20]. Then the ratio between the joint prbability detection and the product of single detection probability is R= P(1,2)/P(1)P(2) = [1+ (1-11) 2COS220]. This formula exibits an oscillation proportional to cos220 and predicts an enhanced joint detection probability which in the case of 0= 0 and rl = 0.1 is 80% larger than the quantm mechanical prediction. REFERENCES Croca, J.R., Garuccio, A., Lepore, V.L. and Moreira, R.N. (1990)Found. Phys. Lett. 3, 557. Croca, J.R., Garuccio, A., Lepore, V.L. and Moreira, R.N. (1992)Phys. Rev. Lett. 68, 3813. de Broglie,L.(1968) Ondes electromagndtique etphotons, Gauthier-Villard, Paris. de Broglie, L. and Andrade a Silva, J.(1968)Phys. Rev. 172, 1284. Pfleegor, R.L., Mandel, L. (1967) Phys Rev. 159, 1084. P; Grangier, G. Roger, and A. Aspect. Europhys. Lett. 1,173 (1986). Selleri, F. (1992) Proceedings of the international conference "Bell's Theorem and the Foundations of Modern Physics" Cesena 1991, Italy in press Wang,L.J,, Zou, X.Y., Mandel, L.(1991)Phys. Rev. Lett. 66, 1111 . Wang,L.J., Zou, X.Y., Mandel, L.(1992)Phys. Rev. Left. 68, 3813.