Universal photonic tunneling time

Aichmann

2015

EPJ Web of Conferences

Abstract. Feynman introduced virtual particles in his diagrams as intermediate states of an interaction process. They represent necessary intermediate states between observable real states. Such virtual particles were introduced to describe the interaction process between an electron and a positron and for much more complicated interaction processes. Other candidates for virtual particles are evanescent modes in optics and in elastic fields. Evanescent modes have a purely imaginary wave number, they represent the mathematical analogy of the tunneling solutions of the Schrödinger equation. Evanescent modes exist in the forbidden frequency bands of a photonic lattice and in undersized wave guides, for instance. The most prominent example for the occurrence of evanescent modes is the frustrated total internal reflection (FTIR) at double prisms. Evanescent modes and tunneling lie outside the bounds of the special theory of relativity. They can cause faster than light (FTL) signal velocities. We present examples of the quantum mechanical behavior of evanescent photons and phonons at a macroscopic scale. The evanescent modes of photons are described by virtual particles as predicted by former QED calculations.

Section: Resultsmentioning

confidence: 99%

“…The calculations of Hartman were confirmed by Refs. [2][3][4][5][6]11], for example. However, as discussed below there are many opposing studies.…”

Section: Introductionmentioning

confidence: 99%

Zero time tunneling: macroscopic experiments with virtual particles

Aichmann

2015

EPJ Web of Conferences

“…The tunneling time is of the order of magnitude of the inverse frequency of the tunneling wave. This property was observed for electromagnetic tunneling [1,2,8]. Recent experimental and theoretical results point to a universal tunneling time for all kinds of fields.…”

mentioning

confidence: 97%

Universal tunneling time for all fields

Stahlhofen

2008

Ann. Phys.

Tunneling is probably the most important physical process. The observation that particles surmount a high mountain in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by the theory of quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies pointed toward a universal tunneling time [1,2]. The observed results and calculations have shown that the tunneling time of opaque photonic barriers (for instance optical mirrors) equals approximately the reciprocal frequency of the electromagnetic wave in question. The tunneling process is described by virtual photons [3]. Virtual particles like photons or electrons are not observable. However, from the theoretical point of view, they represent necessary intermediate states between observable real states. In the case of tunneling there is a virtual particle between the incident and the transmitted particle. Tunneling modes have a purely imaginary wave number. They represent solutions of the Schrödinger equation and of the classical Helmholtz equation. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this pseudo classical optical phenomenon represents the analogy of quantum mechanical tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time independent of the kind of field. Tunneling proceeds at a time of the order of magnitude of the reciprocal frequency of the wave.Optical evanescent modes and solutions of quantum mechanical tunneling have a purely imaginary wave number. This means that they do not experience a phase shift in traversing space. The delay time τ of a propagating wave packet is given by the derivative τ = −dφ/dω,1

“…where the factor A depends on the specific barrier and wave packet in question [21,22]. Recent experimental data on phonon and electron tunneling have pointed to a similar barrier traversal time relation ship [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…The observed tunneling time behavior for certain special barriers provided a theoretical basis for Esposito [21]. He deduced the modified relation…”

Section: Introductionmentioning

confidence: 99%

Erratum to: On Virtual Phonons, Photons, and Electrons

2010

Found Phys

A macroscopic realization of the peculiar virtual particles is presented. The classical Helmholtz and the Schrödinger equations are differential equations of the same mathematical structure. The solutions with an imaginary wave number are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary wave numbers point to strange consequences: The waves are non-local, they are not observable, and they are described as virtual particles. During the last two decades QED calculations of the solutions with an imaginary wave number have been experimentally confirmed for phonons, photons, and electrons. The experimental proofs of the predictions of non-relativistic quantum mechanics and the Wigner phase time approach for the elastic, electromagnetic and Schrödinger fields will be presented in this article. The results are zero time in the barrier and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured tunneling time scalesThe online version of the original article can be found under doi:10.1007/s10701-009-9356-z.G. Nimtz ( ) II. Physikalisches Institut, Universität zu Köln, Zülpicherstrasse 77, 50937 Köln, Germany e-mail: G. Nimtz@uni-koeln.de 1222 Found Phys (2010) 40: 1221-1230 approximately inversely with the particle energy. Actually, the tunneling time is given only by the barrier boundary interaction time, as zero time is spent inside a barrier.