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Physical Review A

Fourth-order interference effects at large distances

John G. Rarity, P. R. Tapster

Published Feb 1, 1992• 57 citations
Publisher

Abstract

We present an experimental demonstration of a fourth-order interference effect first suggested by Franson [Phys. Rev. Lett. 62, 2205 (1989)], where pair photons are directed to two separated Mach-Zehnder interferometers. Apparent nonlocal control of the output ports in which coincident photons are detected can be demonstrated. We show that this effect is present when one of the photons has passed through 170 m of multimode optical fiber. Such a system could form the basis of an interception-proof communication system.

DOI
10.1103/physreva.45.2052

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In recent experiments1 the phenomenon of two-photon interference has been studied, and apparent nonlocal interference effects have been convincingly demonstrated.2 In all these experiments interference effects are not manifest in the singles count rates but appear in the coincidence rate or rate of detection of pair events and are a result of entanglement of the pair photon wavefunction. Modulation of the coincidence rate provides the basis of various covert communications schemes. We have previously demonstrated a free-space propagation communication system using a classical time shift coding out to ranges of 200 m using light levels 1/1000th of ambient daylight levels. This has been extended to a fiber (200-m) based system that exploits nonlocal interference using a scheme first proposed by Franson? With high visibility interference effects single photons can be used to code individual bits of information leading to extremely secure communication.

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We present an experimental demonstration of a fourth-order interference effect first suggested by Franson [Phys. Rev. Lett. 62, 2205 (1989)], where pair photons are directed to two separated Mach-Zehnder interferometers. Apparent nonlocal control of the output ports in which coincident photons are detected can be demonstrated. We show that this effect is present when one of the photons has passed through 170 m of multimode optical fiber. Such a system could form the basis of an interception-proof communication system.
We examine the fourth-order interference properties of two photons at a lossless four-port optical device. The photon pair is represented by a joint single-photon wave-packet state with arbitrary spectral composition. We explicitly determine the coincidence probabilities at the output ports of a beam splitter and a Mach-Zehnder interferometer when the incident wave packet is described by a joint Gaussian spectral distribution and the two photons are incident one at each port of the device. For uncorrelated and distinguishable input photons, the fourth-order interference is readily understood in terms of the particle or wave behavior of each photon acting separately. On the other hand, highly correlated photon pairs, such as those generated from spontaneous parametric down-conversion, exhibit fourth-order interference effects at the output of the interferometer that depend expressly on the joint nature of the photon-pair wave packet, and cannot be described by the particle or wave behavior of either photon.
In a Franson interferometer two-photon interference fringes occur despite the photons never encountering each other [1]. This phenomenon is a fundamental demonstration of the nonlocal nature of quantum mechanics. It serves also as a direct proof of frequency-time-entanglement. Furthermore, it can benefit not only from local, but also nonlocal dispersion cancellation techniques [2], which is a very useful property when working with spectrally broad photon pairs. More specifically, one has to distinguish between dispersion occuring before the individual Mach-Zehnder interferometers (MZIs), which constitute the Franson interferometer, and within them. Analysis of influences up to second order has shown that no loss of contrast can be expected from dispersion before the Franson interferometer. Differential second-order dispersion inside the interferometer, however, can cause a reduction of contrast in the interferogram [3].
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.
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.
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.
In recent experiments1 the phenomenon of two-photon interference has been studied, and apparent nonlocal interference effects have been convincingly demonstrated.2 In all these experiments interference effects are not manifest in the singles count rates but appear in the coincidence rate or rate of detection of pair events and are a result of entanglement of the pair photon wavefunction. Modulation of the coincidence rate provides the basis of various covert communications schemes. We have previously demonstrated a free-space propagation communication system using a classical time shift coding out to ranges of 200 m using light levels 1/1000th of ambient daylight levels. This has been extended to a fiber (200-m) based system that exploits nonlocal interference using a scheme first proposed by Franson? With high visibility interference effects single photons can be used to code individual bits of information leading to extremely secure communication.