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American Journal of Physics

Dirac and Photon Interference

Robert J. Sciamanda

Published Nov 1, 1969• 1 citation
Publisher

Abstract

Students' difficulties in applying a statement of Dirac to two-laser interference should have been brought up in connection with many of the traditional beam-splitting experiments, which also involve more than one source. The temptation to add intensities rather than wavefunctions is a throw-back to the classical concept of distinguishable particles, and the intuitive feeling that one can divide radiating matter into distinct sources, each emitting distinct photons.

DOI
10.1119/1.1975229

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Students' difficulties in applying a statement of Dirac to two-laser interference should have been brought up in connection with many of the traditional beam-splitting experiments, which also involve more than one source. The temptation to add intensities rather than wavefunctions is a throw-back to the classical concept of distinguishable particles, and the intuitive feeling that one can divide radiating matter into distinct sources, each emitting distinct photons.
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Using a selection of key experiments performed over the past 30 years or so, we present a discussion of the strikingly counter-intuitive phenomena of the quantum world that defy explanation in terms of everyday "common sense" reasoning, and we provide the corresponding quantum mechanical explanations with a very elementary use of associated formalism. Most, but certainly not all, of the experiments we describe are optical experiments involving a very small number of photons (particles of light). We begin with experiments on the wave-particle duality of electrons, proceed to experiments on the particle nature of light and single photon interference, delayed choice experiments and interaction-free detection, then go on to experiments involving the interference of two photons, quantum entanglement and Bell's Theorem, quantum teleportation, large-scale quantum effects and the divide between the classical and quantum worlds, addressing the question as to whether or not there is such a divide.
The interference of the beams of light led to the foundations of wave optics and this motivated founding fathers of quantum mechanics to arrive at the wave equation for quantum particles like electrons. With the advent of quantum theory of light by Planck, Dirac pondered over how the interference would arise with single photons as these fundamental entities could not be broken in two parts like light waves. He introduced the idea of the quantum amplitudes for the paths which needed to be summed up coherently before finding the intensity or the photon detection probability. I will present a very important application of the interference among several paths to understand in clear physical terms the phenomena of super radiance ie the emergence of enhanced radiation from a system initially prepared in a collective state. I will show how how a collective state leads to several paths along which photon can be emitted. A constructive interference of these paths leads to super radiance where as a destructive interference leads to sub radiance.
The genesis of quantum optics can be found in the Dirac discussion on interference as disclosed in The Principles of Quantum Mechanics . This is a masterful and prophetic discussion that begins by considering a roughly monochromatic light source. The discussion continues by considering a beam of light consisting of a large number of photons. Besides Dirac, useful references on interferometry include Steel, Meaburn and Born and Wolf. The Hanbury Brown–Twiss effect originates in interferometric measurements performed by an “intensity interferometer” used for astronomical observations. A diagram of the stellar intensity interferometer used to determine the diameter of stars is depicted. Two-beam interferometers are optical devices that divide and then recombine a light beam. It is on recombination of the beams that interference occurs. The most well-known two-beam interferometers are the Sagnac interferometer, the Mach–Zehnder interferometer, and the Michelson interferometer.
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.