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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Significance of Interference between Two Independent Attenuated Laser Beams

Benjamin Liebowitz

Published Jan 15, 1970• 3 citations
Publisher

Abstract

Pfleegor and Mandel produced interference effects from two separate independent laser beams when the quanta arriving at the detector were separated in time by an average of about 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ sec. If the quanta are photons (particles), then, to produce interference, each photon must store energy in the detector for an average of at least 1.4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ sec. But J\'anossy and N\'aray have recently shown that over a period of 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec there is no such storage, at least when the phases are random. Thus the result of Pfleegor and Mandel is in conflict with the corpuscular concept of visible light.

DOI
10.1103/physrevd.1.720

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Pfleegor and Mandel produced interference effects from two separate independent laser beams when the quanta arriving at the detector were separated in time by an average of about 1.4\ifmmode\times\else\texttimes\fi{}10\ensuremath−7{10}^{\ensuremath{-}7}10\ensuremath−7 sec. If the quanta are photons (particles), then, to produce interference, each photon must store energy in the detector for an average of at least 1.4\ifmmode\times\else\texttimes\fi{}10\ensuremath−7{10}^{\ensuremath{-}7}10\ensuremath−7 sec. But J'anossy and N'aray have recently shown that over a period of 9\ifmmode\times\else\texttimes\fi{}10\ensuremath−9{10}^{\ensuremath{-}9}10\ensuremath−9 sec there is no such storage, at least when the phases are random. Thus the result of Pfleegor and Mandel is in conflict with the corpuscular concept of visible light.
The Pfleegor-Mandel experiment showing the interference between two beams coming from two independent lasers is reviewed. It is argued that the interference fringes detected by Pfleegor and Mandel may not be caused by the interference, which is an interaction between the two beams. Instead of the interference between the two beams coming from two lasers, the following is suggested. The photons coming from the first laser interact with the environment of the path leading from the second laser, and the photons coming from the second laser interact with the environment of the path leading from the first laser. A modification of the Pfleegor-Mandel experiment that eliminates the possible interaction with the path from the other laser is proposed.
We extend and generalize previous work on the interference of light from independent cavities that began with the suggestion of Pfleegor and Mandel [Phys. Rev. 159, 1084 (1967)] that their observed interference of laser beams should not be associated too closely with particular states of the beams but more with the detection process itself. In particular we examine how the detection of interference induces a nonrandom-phase difference between internal cavity states with initial random phases for a much broader range of such states than has previously been considered. We find that a subsequent interference measurement should give results consistent with the induced phase difference. The inclusion of more cavities in the interference measurements enables the construction in principle of a laboratory in the sense used by Aharonov and Susskind, made up of cavity fields that can serve as frames of phase reference. We also show reasonably simply how intrinsic phase coherence of a beam of light leaking from a single cavity arises for any internal cavity state, even a photon number state. Although the work presented here may have some implications for the current controversy over whether or not a typical laboratory laser produces a coherent state, it is not the purpose of this paper to enter this controversy; rather it is to examine the interesting quantum physics that arises for cavities with more general internal states.
The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.
Interference fringes produced by the superposition of light beams from two independent lasers have been investigated under conditions where the light flux was so low that one photon was usually received at the detector before the next one was emitted by one or the other source. Because the average number of photons detected in each observation was only about 10, a photon correlation technique was used to demonstrate the presence of interference fringes. The measurement procedure was automated, and this led to much greater statistical accuracy than was previously reported. The effect of varying the observation time and the number of interference fringes sampled was investigated, and found to be in good agreement with theory.
Interference effects produced by the superposition of the light beams from two independent single-mode lasers have been investigated experimentally. It is found that interference takes place even under conditions in which the light intensities are so low that, with high probability, one photon is absorbed before the next one is emitted by one or the other source. Since the average number of registered photons per trial was only about 10, photon correlation techniques were required to demonstrate the interference. The interpretation of the experiment, and the question whether it demonstrates interference between two photons, are discussed.