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AIP conference proceedings

Non-classical interference experiments with photon pairs

L. Mandeļ

Published Jan 1, 1991• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.40962

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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.
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.
A new fourth-order interference experiment based on detecting photon pairs in coincidence has been carried out. A Mach-Zehnder type of interferometer is used, with the two photons generated simultaneously in the process of down-conversion as inputs and two photon counting detectors at the two outputs. The optical path difference can be varied piezoelectrically. It is found that the coincidence counting rate, after subtraction of accidentals, exhibits a sinusoidal variation with the optical path difference as predicted by quantum mechanics, but in violation of the laws of classical optics. This is another non-classical interference effeet. By contrast, two light beams derived from a He:Ne laser used as inputs to the interferometer, do not produce any fourth order interference.
Optical interference is regarded as a classical phenomenon and is usually completely described in classical terms, in which optical fields are represented by classical waves. Does it mean that optical interference, which is fundamentally ascribable to the phenomenon of a superposition of wave amplitudes, cannot be applied to test quantum phenomena? The superposition principle is at the heart of quantum physics and one could expect that it should distinguish the quantum nature of light from thewave nature. Our experience based on extensive theoretical analysis and experimental observations shows that classical and quantum theories of optical interference readily explain the presence of an interference pattern resulting from the first-order coherence. However, there are interference effects involving the higher order (second-order) coherence that distinguish the quantum (photon) nature of light from the wave nature. Quantum interference has recently returned to prominence because of its utility in manipulating spontaneous emission and other radiative properties of atomic systems. In this chapter, we present elementary concepts and definitions of both the classical and quantum theory of optical interference and discuss similarities and differences between these two approaches [80].
This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.