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arXiv:0903.2582

Tunneling: From Milliseconds to Attoaseconds

Guenter Nimtz

Published Mar 14, 2009• 1 citation
arXivHTMLPDF

Abstract

How much time does a wave packet spent in tunneling a barrier? Quantum mechanical calculations result in zero time inside a barrier. In the nineties analogous tunneling experiments with microwaves were carried out confirming quantum mechanics. Electron tunneling time is hard to measure being extremely short. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now. It appears that the tunneling time is a universal property in the investigated time range of twelve orders of magnitude.

DOI
10.48550/arxiv.0903.2582

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How much time does a wave packet spent in tunneling a barrier? Quantum mechanical calculations result in zero time inside a barrier. In the nineties analogous tunneling experiments with microwaves were carried out confirming quantum mechanics. Electron tunneling time is hard to measure being extremely short. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now. It appears that the tunneling time is a universal property in the investigated time range of twelve orders of magnitude.
How much time does a tunneling wave packet spent in traversing a barrier? Quantum mechanical calculations result in zero time inside a barrier . In the nineties analogous tunneling experiments with microwaves were carried out. The results agreed with quantum mechanical calculations. Electron tunneling time is hard to measure being extremely short and parasitic effects due to the electric charge of electrons may be dominant. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now and will be presented. It appears that the tunneling time is a universal property independent of the field in question.
We begin the Article with confusing citations in published papers on the question recently: how much time does a wave packet spend in a tunnelling barrier? ..a particle tunnelling through a barrier appears to do so in zero time 1. .. The pulse transit through the barrier itself seems to be instantaneous 2. ..tunnelling is unlike to be an instantaneous process 3. ..ionization time is close to zero 4. ..all waves have a zero tunneling time [5]. ..Our results are inconsistent with claims that tunnelling takes zero time 6
Abstract Zero tunneling time and thereby a faster than light traversal velocity was calculated nearly a hundred years ago and has been observed recently. We report about experimental results and estimations, which confirm the zero time tunneling for elastic as well as for electromagnetic and Schrödinger waves. Zero time tunneling was first observed with microwaves 1992 (H. Aichmann and G. Nimtz, Found. Phys., vol. 44, p. 678, 2014; A. Enders and G. Nimtz, J. Phys. I, vol. 2, p. 169, 1992). In 2008, zero time was also observed for tunneling electrons (P. Eckle, A. N. Pfeiffer, C. Cirelli, et al., Science, vol. 322, p. 1525, 2008). Presumably, this effect took place with atoms quite recently (R. Ramos, D. Spierings, I. Racicot, and A. M. Steinberg, Nature, vol. 583, p. 529, 2020). The Einstein relation E 2 = (ħk)2 c 2 is not satisfied in the tunneling process, since the wave number k is imaginary (E is the total energy, ħ the Planck constant, and c the vacuum velocity of light), Zero time tunneling is described by virtual photons (A. Stahlhofen and G. Nimtz, Europhys. Lett., vol. 76, p. 189, 2006). The tunneling process itself violates the Special Theory of Relativity. Remarkably, Brillouin conjectured that wave mechanics is valid for all waves independent of their field (L. Brillouin, Wave Propagation in Periodic Structures, Chap. VIII, New York, Dover Publications, 1953).
Abstract Tunneling is an outstanding physical process. The observation that particles surmount a high barrier 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 quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. 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 optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.
Abstract Since 1931, the nonclassical process of tunneling was conjectured to have a zero-time delay in the barrier. These theories have been rejected and denied. However, photonic and recent electronic tunneling experiments have proven the zero-time prediction. Tunneling is due to virtual wave packets in electromagnetic, elastic, and Schrödinger wave fields up to the macroscopic level. In this article we cite theoretical and experimental studies on zero-time tunneling, which have proven this striking behavior.
Tunneling is an outstanding physical process. The observation that particles surmount a high barrier 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 quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. 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 optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.