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Annalen der Physik

Superluminal propagation of evanescent modes as a quantum effect

Z.‐Y. Wang, C.‐D. Xion, Bing He

Published May 13, 2008• 4 citations
Publisher

Abstract

Abstract Contrary to mechanical waves, the two‐slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum‐field‐theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.

DOI
10.1002/andp.20085200505

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Superluminal propagation of evanescent modes as a quantum effect

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The tunneling of particles is in direct analogy with the transmission of evanescent electromagnetic waveguide modes as has been shown quite recently. We compare experimental data of an electromagnetic wave packet traversing an evanescent waveguide region with theoretical values derived for particle tunneling through a rectangular potential barrier. The transmission time was deduced by transformation of the experimental frequency data to the time domain. The data are in agreement and reveal superluminal wave-packet velocities for opaque evanescent regions.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1993•206 citations
Abstract Contrary to mechanical waves, the two‐slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum‐field‐theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.
Contrary to mechanical waves, the two-slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum-field-theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval without destroying causality. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.
Though both theoretical and experimental investigations have revealed the superluminal behavior of evanescent electromagnetic waves, there are many disputes about the physical meaning and validity of such superluminal phenomenon, which is due to the fact that the traditional investigations are based on the theory of tunneling time and concerned with the problem of what the group velocity of evanescent waves means. In this paper, by studying the quantum probability amplitude for photons to propagate over a spacelike interval along an undersized waveguide, we present theoretical evidence for such superluminality.
Applying the fact that guided photons inside a waveguide can be treated as massive particles, one can study the superluminality of evanescent modes via showing that a massive particle can propagate over a spacelike interval, which corresponds to quantum tunneling effects. For this purpose, we treat the particle as a quantum reference frame, while attach an inertia observer to a classical reference frame, and then quantize the formulae for the Lorentz transformation between the quantum and classical reference frames, from which we obtain the conclusion that, owing to the Heisenberg's uncertainty relation, the particle can propagate over a spacelike interval.
The quantum mechanical tunneling effect was theoretically described in the first half of the last century, which witnessed the rise of quantum theory and groundbreaking experimental results in nuclear physics. A similar tunneling effect also takes place in the case of EM waves. The wave account (in the case of evanescent waves), the quantum-mechanical formalism, as well as the electrodynamical one, revealed a phenomenon that is counterintuitive and possibly even inconsistent with the special relativity theory paradigm. In the quantum formalism, the time of wave propagation within a photonic barrier is expressed as an imaginary number, which can be interpreted as the zero speed of propagation. In the nineties, scientists offered further experimental proofs of the theory; in experimental systems constructed for testing EM-waves tunneling, superluminal speed of propagation has been recorded. In the article, I introduce the problem of photon tunneling in the experimental context of the possibility of nonlocal wave propagation and superluminal transmission of information.
The tunneling of particles is in direct analogy with the transmission of evanescent electromagnetic waveguide modes as has been shown quite recently. We compare experimental data of an electromagnetic wave packet traversing an evanescent waveguide region with theoretical values derived for particle tunneling through a rectangular potential barrier. The transmission time was deduced by transformation of the experimental frequency data to the time domain. The data are in agreement and reveal superluminal wave-packet velocities for opaque evanescent regions.