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Developments in time analysis of particle and photon tunneling

V. S. Olkhovsky, A. Agresti

Published Dec 6, 1996• 3 citations
OpenAlex

Abstract

A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed. The problem of superluminal group velocities, without violations of special relativity, is also taken in account. Then a particular attention is devoted to the presentation of new results on the analogy between particle and photon tunnelling and analysis of the causality validity during tunnelling. [PACS nos. 03.40.Kf, this http URL, 41.20.Jb, this http URL, this http URL, 03.30.+p, 03.65.-w].

Related papers

Developments in time analysis of particle and photon tunnelling

V. S. Olkhovsky, A. Agresti

A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed. The problem of superluminal group velocities, without violations of special relativity, is also taken in account. Then a particular attention is devoted to the presentation of new results on the analogy between particle and photon tunnelling and analysis of the causality validity during tunnelling. [PACS nos. 03.40.Kf, 03.50.De, 41.20.Jb, 41.20.Bt, 42.25.Bs, 03.30.+p, 03.65.-w].

arXiv:physics/9612004•Dec 6, 1996•0 citations

Unified Time Analysis of Photon and (Nonrelativistic) Particle Tunnelling, and the Superluminal Group-Velocity Problem

Jacek Jakiel, V. S. Olkhovsky, Erasmo Recami

A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect (independence of the Tunnelling Time of the opaque barrier width, with Superluminal group velocities as a consequence) is verified for all the known expressions of the mean tunnelling time. Moreover, the analogy between particle and photon tunnelling is suitably exploited. On the basis of such an analogy, an explanation of some recent microwave and optics experimental results on tunnelling times is proposed. Attention is devoted to some aspects of the causality problem for particle and photon tunnelling.

•Apr 30, 2001•0 citations

Quantum Optical Studies of Tunneling and other Superluminal Phenomena

R. Y. Chiao, Aephraim M. Steinberg

Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.

Physica Scripta•Jan 1, 1998•18 citations

On Superluminal Photonic Tunnelling

Günter Nimtz, Astrid Haibel, A. A. Stahlhofen

Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.

Kluwer Academic Publishers eBooks•Dec 23, 2005•2 citations

Tunneling Times and Superluminality: a Tutorial

R. Y. Chiao

Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric down-conversion light source, which produced correlated, but random, emissions of photon pairs. The two photons of a given pair were emitted in slightly different directions so that one photon passed through the tunnel barrier, while the other photon passed through the vacuum. The time delay for the tunneling photon relative to its twin was measured by adjusting the path length difference between the two photons in a Hong-Ou-Mandel interferometer, in order to achieve coincidence detection. We found that the photon transit time through the barrier was smaller than the twin photon’s transit time through an equal distance in vacuum, indicating that the process of tunneling in quantum mechanics is superluminal. Various conflicting theories of tunneling times are compared with experiment. An introduction to an introduction Tunneling, the quantum mechanical process by which a particle can penetrate a classically forbidden region of space, is one of the most mysterious phenomena of quantum mechanics. Yet it is one of the most basic and important processes in Nature, without which we could not even exist, for tunneling is involved in the very first step of the nuclear reaction, p + p → d + e + νe, which powers the Sun, the source of energy for life on the Earth. ∗ On appointment as a Miller Research Professor in the Miller Institute for Basic Research

•Jan 1, 1999•15 citations

Tempi di Tunnelling (Tunneling Times)

Giuseppe Privitera, Erasmo Recami, V. S. Olkhovsky

In this review (in Italian) we critically and detaily examine various definitions existing in the literature for the tunnelling times: namely, the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and the generalized (Olkhovsky and Recami) dwell time, with some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and "photon tunnelling" (evanescent waves propagation), with particular attention to tunnellings with Superluminal group-velocities ("Hartman effect"). At last, the main (Cologne, Berkeley, Florence, Vienna) experimental data about Superluminal evanescent wave propagation are briefly reviewed.

arXiv:cond-mat/9802126•Feb 11, 1998•0 citations
A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed. The problem of superluminal group velocities, without violations of special relativity, is also taken in account. Then a particular attention is devoted to the presentation of new results on the analogy between particle and photon tunnelling and analysis of the causality validity during tunnelling. [PACS nos. 03.40.Kf, this http URL, 41.20.Jb, this http URL, this http URL, 03.30.+p, 03.65.-w].
A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed. The problem of superluminal group velocities, without violations of special relativity, is also taken in account. Then a particular attention is devoted to the presentation of new results on the analogy between particle and photon tunnelling and analysis of the causality validity during tunnelling. [PACS nos. 03.40.Kf, 03.50.De, 41.20.Jb, 41.20.Bt, 42.25.Bs, 03.30.+p, 03.65.-w].
A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect (independence of the Tunnelling Time of the opaque barrier width, with Superluminal group velocities as a consequence) is verified for all the known expressions of the mean tunnelling time. Moreover, the analogy between particle and photon tunnelling is suitably exploited. On the basis of such an analogy, an explanation of some recent microwave and optics experimental results on tunnelling times is proposed. Attention is devoted to some aspects of the causality problem for particle and photon tunnelling.
Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.
Evanescent modes or the tunnelling process are characterized by an imaginary wave number. These special solutions of the Helmholtz and of the Schrödinger equations first noticed in connection with the total reflection were said to have no physical meaning about 200 years ago. Last century the tunnelling problem in quantum mechanics has been described by the phase time approach. The phase time approach yields the group velocity of a wave packet (see e.g. Hartman, 1962). Nowadays the phase time approach is used in network analyzers to determine the group velocity of an electromagnetic wave in devices. We have reported about superluminal signal velocities in photonic tunnelling. It was observed that the superluminal photonic tunnelling time data measured in the time domain are in agreement with the calculated phase time data. This result is also in agreement with the definition of the barrier transition time given in the Federal Standard 1037 C (NTIA, USA 2000). Thus we have added further credibility to the assumption that the photonic tunnelling results are representative for quantum mechanical tunnelling of particles.
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric down-conversion light source, which produced correlated, but random, emissions of photon pairs. The two photons of a given pair were emitted in slightly different directions so that one photon passed through the tunnel barrier, while the other photon passed through the vacuum. The time delay for the tunneling photon relative to its twin was measured by adjusting the path length difference between the two photons in a Hong-Ou-Mandel interferometer, in order to achieve coincidence detection. We found that the photon transit time through the barrier was smaller than the twin photon’s transit time through an equal distance in vacuum, indicating that the process of tunneling in quantum mechanics is superluminal. Various conflicting theories of tunneling times are compared with experiment. An introduction to an introduction Tunneling, the quantum mechanical process by which a particle can penetrate a classically forbidden region of space, is one of the most mysterious phenomena of quantum mechanics. Yet it is one of the most basic and important processes in Nature, without which we could not even exist, for tunneling is involved in the very first step of the nuclear reaction, p + p → d + e + νe, which powers the Sun, the source of energy for life on the Earth. ∗ On appointment as a Miller Research Professor in the Miller Institute for Basic Research
In this review (in Italian) we critically and detaily examine various definitions existing in the literature for the tunnelling times: namely, the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and the generalized (Olkhovsky and Recami) dwell time, with some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and "photon tunnelling" (evanescent waves propagation), with particular attention to tunnellings with Superluminal group-velocities ("Hartman effect"). At last, the main (Cologne, Berkeley, Florence, Vienna) experimental data about Superluminal evanescent wave propagation are briefly reviewed.