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Journal of the Optical Society of America B

Classical treatment of the Franson two-photon correlation experiment

Z. Y. Ou, L. Mandeļ

Published Oct 1, 1990• 17 citations
Publisher

Abstract

A two-photon correlation experiment that was proposed by Franson [ Phys. Rev. Lett.62, 2205 ( 1989)] and was recently carried out is analyzed in terms of electromagnetic waves in order to see whether the observed fourth-order interference effects can be explained classically. The conclusion is that, although a classical field can give rise to such interference effects, no classical field can actually account for the observations reported.

DOI
10.1364/josab.7.002127

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AIP conference proceedings•Jan 1, 1991•0 citations
A two-photon correlation experiment that was proposed by Franson [ Phys. Rev. Lett.62, 2205 ( 1989)] and was recently carried out is analyzed in terms of electromagnetic waves in order to see whether the observed fourth-order interference effects can be explained classically. The conclusion is that, although a classical field can give rise to such interference effects, no classical field can actually account for the observations reported.
A two-photon correlation experiment of the kind that was proposed by Franson and has recently been carried out by two groups is analyzed. In this experiment two simultaneously produced photons are directed along two paths to two photodetectors without mixing. An unbalanced interferometer with delay time that is much longer than the coherence time of the light is inserted in each path. Yet the rate of two-photon detection by the two detectors in coincidence exhibits interference as the path difference is changed. The question of whether classical field theory can account for these observations is discussed. We show that no ergodic classical field is able to reproduce the experimental results, although a nonergodic field can give rise to interference through the artifice of generating an ensemble by initializing repeatedly.
Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.
The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.
Models of a two-photon interference experiment proposed by Franson to study the Einstein-Podolsky-Rosen (EPR) effect are presented. The experiment considers a pair of photons correlated in time and in frequency, each of which is passed through an interferometer. When the path difference through the two interferometers is set so there is no first-order interference, Franson showed that second-order interference between the two photons could occur with 100% visibility. In this paper both quantum and classical models are considered and the importance of the coincidence time window and the effect of the frequency correlation are shown. Calculations are presented for all settings of the interferometers. The EPR effect arises from entangled states; a brief discussion is given of the nature of the entangled state for this type of experiment.
A new fourth-order interference experiment has been carried out and analyzed theoretically in classical and in quantum terms. Two photons produced in the process of parametric down-conversion provide the two inputs to a Mach-Zehnder type of interferometer, while two photodetectors coupled to a coincidence counter measure the output. The coincidence rate, after subtraction of accidentals, exhibits a cosine variation with the optical path difference, in agreement with quantum mechanics, but in disagreement with a classical analysis. By contrast, when two coherent light beams from a He:Ne laser are used as inputs to the interferometer, no fourth-order interference is observed.
Although interference of light is commonly regarded as a classical wave phenomenon, interesting fourth‐order interference effects are exhibited by correlated photon pairs, which violate classical probability. The effects manifest themselves in that the visibility is larger than allowed by classical theory, or the interference is independent of the light intensity, in violation of classical theory. In some situations classical optics predicts no interference at all, whereas quantum optics does. The interference technique has been used to measure time intervals between two photons with fsec resolution. Several examples of experiments in which non‐classical interference effects were observed will be described.