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ISRN Spectroscopy

Periodic Variations in the Wavelength Distributions following Photon Interferences: Analogy with Electron Interferences

Maxime Vabre, Sylvain Girard, H. Gilles, B S Frankland, F. Porée, P. Leprince, J.-Y. Chesnel, R O Barrachina, F. Frémont

Published Feb 19, 2012• 3 citations
Publisher

Abstract

A new interference phenomenon is reported, which has so far not been observed with either matter or light. In a nanometer-sized version of Feynman's famous two-slit “thought” experiment with single electrons, the width of a quasi-monochromatic line has been found to oscillate with the detection angle. Since this experiment resembles the original double-slit experiment by Young with light (1807), photon interferences were investigated in order to determine the wavelength distribution as a function of the position in the interference field. In addition to the well-known oscillating dependence of the intensity with a succession of dark and bright fringes, a periodic dependence with respect to the detection position has also been observed for the width of the wavelength distribution, revealing a larger analogy between electron and photon interferences.

DOI
10.5402/2012/174952

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A new interference phenomenon is reported, which has so far not been observed with either matter or light. In a nanometer-sized version of Feynman's famous two-slit “thought” experiment with single electrons, the width of a quasi-monochromatic line has been found to oscillate with the detection angle. Since this experiment resembles the original double-slit experiment by Young with light (1807), photon interferences were investigated in order to determine the wavelength distribution as a function of the position in the interference field. In addition to the well-known oscillating dependence of the intensity with a succession of dark and bright fringes, a periodic dependence with respect to the detection position has also been observed for the width of the wavelength distribution, revealing a larger analogy between electron and photon interferences.
In this article we provide experimental evidence of an interference phenomenon that, to the best of our knowledge, has so far not been observed with either matter or light. In a nanometer-sized version of Feynman's famous two-slit ``thought'' experiment with single electrons, we managed to observe that the width of a quasi-monochromatic line oscillates with the detection angle. Furthermore, we find that it occurs in counterphase with the line intensity. We discuss the underlying mechanism that produces this unexpected result.
3.1 Interference of a Single Photon The kinds of study originally conducted by Thomas Young - in particular, the celebrated "double slit" experiment that we briefly examined in Chapter 1 (see Fig. 1) - provide a capacity to reveal far more than the wave nature of light, important as that is. True enough, the observed characteristic fringe pattern, when monochromatic light passes through two closely spaced slits onto a screen, appears to be simply explicable on the basis of waves from each slit undergoing constructive and destructive interference at different positions on the screen. Yet, astonishingly, these patterns of interference are still exhibited when individual photons of a low-intensity input beam reach the screen one at a time, showing that it cannot in fact be a matter of different photons having to interfere with each other. Indeed, Dirac enunciated the general principle that photons can never directly interact with each other. The double slit and other such experiments indicate that each photon interacts in a delocalized, wave-like manner with both slits at the same time. Successive experiments build interference patterns that conform to an exact mathematical distribution formula, but the position at which an individual photon is detected in any particular instance cannot be predicted; this is a quintessential illustration of quantum uncertainty. Using the path integral approach of quantum theory, the phenomenon is more accurately represented by introducing a summation over all possible routes between the source and the screen on which the pattern appears, signifying an entire "lifetime" for each photon involved in the experiment. This relates to the fact that the actual trajectory is unknown without an observation, and thus we only obtain the probabilities of the photon striking the screen at different positions and times; all trajectories (potentialities) must be considered in a superposition. Each route is considered equally probable, and the variation in phase produces quantum interference. The differences in phase of each trajectory, at varying positions on the screen, generates the fringe pattern. An intriguing variation on this experiment involves "marking" the photons so that the actual route of each photon to the screen is known. Remarkably, in such a case, the fringe patterns do not appear because quantum interference cannot occur. A consequence of the observation of the photon route is an effect that, in other quantum mechanical connections, is known as a collapse of the wavefunction. However, it is possible for the fringe patterns to reappear when information on the route of the photons is lost; this is known as a quantum eraser.
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete interference information about two colors. The conceptual model provides an intuitional picture of the in-phase and out-of-phase photon correlations and a complete quantum understanding about the which-path information of two colored photons.
Young’s double slit experiment revived the wave theory of the light. The standard interpretation is that the light behaves as waves before and after passing through the diaphragm of the double slit. Feynman called the double slit experiment the only mystery in quantum mechanics. Recently, the photon chamber has been proposed and utilized to study the behavior of photons near the detecting screen. The experiments show that the light, near the screen, behaves as photons propagating along the straight-line trajectories, and the trajectories distribute as waves. Furthermore, the photon chamber experiments show that, withing a macroscopic distance from the double slit, the pattern is non-interference, which indicates that the standard double slit experiments violate the standard wave interpretations in the area near the diaphragm. In this article, we utilize two new methods to study how the non-interference pattern (near the double slit) evolving to the interference pattern (far from it). The experiments show, the first time, that (1) the shape of the pattern are distance-dependent, when the distance increases, the non-interference pattern evolves to the interference pattern, which indicates that the non-wave nature and the wave distribution coexist in the same wave experiment; (2) the light beams behave as photons near the double slit. The experiments: (1) provide novel phenomena/data for further theoretical development of the established optics and for understanding the nature of the light; (2) show the Feynman’s mystery in the different perspectives; (3) provide three methods that show the non-wave pattern in standard wave experiments and can be utilized to develop the classical optics further.
Interference is a classic property of waves. It can be seen most clearly when a coherent wave is split into two partial waves that are then recombined to produce periodic variations in the measured intensity. These variations can be observed directly as a pattern of bright and dark interference fringes on a screen. The classic interferometer set-up is the Young's double-slit experiment: a small light source emitting in a narrow frequency band is placed on one side of the slits, and an interference pattern is observed at the screen on the other side (figure a). The fringes are bright where the partial waves interfere constructively, and dark where the interference is destructive.