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Physical Review A

“Superluminal” tunneling as a weak measurement effect

D. Sokolovski, ALFRED Z. MSEZANE, Vasily R. Shaginyan

Published Jun 21, 2005• 33 citations
Publisher

Abstract

We exploit the analogy between the transfer of a pulse across a scattering medium and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly ``superluminal'' behavior of a tunneling particle in the barrier or a photon in a ``fast-light'' medium. We demonstrate that superluminality occurs when the value of the duration $\ensuremath{\tau}$ spent in the barrier is uncertain, whereas when $\ensuremath{\tau}$ is known accurately, no superluminal behavior is observed. In all cases only subluminal durations contribute to the transmission which precludes faster-than-light information transfer, as observed in a recent experiment.

DOI
10.1103/physreva.71.064103

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arXiv:1405.3364•May 14, 2014•0 citations
We exploit the analogy between the transfer of a pulse across a scattering medium and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly superluminal'' behavior of a tunneling particle in the barrier or a photon in a fast-light'' medium. We demonstrate that superluminality occurs when the value of the duration \ensuremathτ\ensuremath{\tau}\ensuremathτ spent in the barrier is uncertain, whereas when \ensuremathτ\ensuremath{\tau}\ensuremathτ is known accurately, no superluminal behavior is observed. In all cases only subluminal durations contribute to the transmission which precludes faster-than-light information transfer, as observed in a recent experiment.
We exploit the analogy between tunnelling across a potential barrier and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly 'superluminal' behaviur of the tunnelling particle in the barrier. We demonstrate that 'superluminality' occurs when the value of the duration τττ spent in the barrier is uncertain, whereas when τττ is known accurately, no 'superluminal' behaviur is observed. In all cases only subluminal durations contribute to the transmission, which precludes faster-than-light information transfer, as shown by a recent experiment.
We exploit the analogy between tunnelling across a potential barrier and Aharonov's weak measurements to resolve the long standing paradox between the impossibility to exceed the speed of light and the seemingly 'superluminal' behaviur of the tunnelling particle in the barrier. We demonstrate that 'superluminality' occurs when the value of the duration tau\\tautau spent in the barrier is uncertain, whereas when tau\\tautau is known accurately, no 'superluminal' behaviur is observed. In all cases only subluminal durations contribute to the transmission across the barrier.
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.