Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Reshaping, path uncertainty, and superluminal traveling

Wang Yun-ping, Zhang Dian-lin

Published Oct 1, 1995• 35 citations
Publisher

Abstract

It is shown that when the wave packet of a photon passes through a region where more than one path mode can be chosen, the interference between these modes of the probability waves of the photon causes a reshaping process of the wave packet. In some conditions this reshaping gives rise to an apparent superluminal traveling, as observed by Steinberg, Kwiat, and Chiao [Phys. Rev. Lett. 71, 708 (1993)]. The present model also leads to some predictions that can be tested experimentally.

DOI
10.1103/physreva.52.2597

Related papers

Explanation of Superluminal Phenomena Based on Wave-Particle Duality and Proposed Optical Experiments

Hai-Long Zhao

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.

arXiv:1405.3364•May 14, 2014•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

Quantum noise and superluminal propagation

Bilha Segev, Peter W. Milonni, J. F. Babb +1 more

Causal ``superluminal'' effects have recently been observed and discussed in various contexts. The question arises whether such effects could be observed with extremely weak pulses, and what would prevent the observation of an ``optical tachyon.'' Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett. 81, 2190 (1998)] have argued that quantum noise will preclude the observation of a superluminal group velocity when the pulse consists of one or a few photons. In this paper we reconsider this question both in a general framework and in the specific example, suggested by Chiao, Kozhekin, and Kurizki (CKK) [Phys. Rev. 77, 1254 (1996)], of off-resonant, short-pulse propagation in an optical amplifier. We derive in the case of the amplifier a signal-to-noise ratio that is consistent with the general ARS conclusions when we impose their criteria for distinguishing between superluminal propagation and propagation at the speed c. However, results consistent with the semiclassical arguments of CKK are obtained if weaker criteria are imposed, in which case the signal can exceed the noise without being ``exponentially large.'' We show that the quantum fluctuations of the field considered by ARS are closely related to superfluorescence noise. More generally, we consider the implications of unitarity for superluminal propagation and quantum noise and study, in addition to the complete and truncated wave packets considered by ARS, the residual wave packet formed by their difference. This leads to the conclusion that the noise is mostly luminal and delayed with respect to the superluminal signal. In the limit of a very weak incident signal pulse, the superluminal signal will be dominated by the noise part, and the signal-to-noise ratio will therefore be very small.

arXiv:quant-ph/0004047•Physical Review A•Jul 19, 2000•34 citations

Superluminal traversal time and interference between multiple finite wave packets

Xi Chen, Chun-Fang Li

The mechanism of superluminal traversal time is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparison with a characteristic length of the incident wave packet, the reshaped wave packet with superluminal traversal time in transmission maintains the pro. le of the incident wave packet. In the case of potential barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier thickness dependence of the traversal time for thin barriers and its barrier thickness independence for thick barriers. This manifests the nature of the Hartman effect. Copyright (c) EPLA, 2008.

arXiv:quant-ph/0611154•Europhysics Letters (EPL)•Apr 21, 2008•13 citations

Superluminal delays of coherent pulses in nondissipative media: A universal mechanism

Yonathan Japha, Gershon Kurizki

We identify the universal mechanism that is responsible for superluminal (faster-than-light) traversal times as well as the narrowing of wave packets transmitted through various nondissipative media. This mechanism is shown to be predominantly destructive interference between successive wave-packet components traversing all accessible causally retarded paths. It strongly depends on wave-packet coherence and width, and can cause superluminal traversal not only in evanescent-wave ``tunneling'' but also in allowed propagation. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jan 1, 1996•92 citations

Superoscillations and tunneling times

Yakir Aharonov, Noam Erez A, Benni Reznik

It is proposed that superoscillations play an important role in the interferences that give rise to superluminal effects. To exemplify that, we consider a toy model that a wave packet to travel in zero time and negligible distortion, a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time.

arXiv:quant-ph/0110104•Physical Review A•May 17, 2002•79 citations
It is shown that when the wave packet of a photon passes through a region where more than one path mode can be chosen, the interference between these modes of the probability waves of the photon causes a reshaping process of the wave packet. In some conditions this reshaping gives rise to an apparent superluminal traveling, as observed by Steinberg, Kwiat, and Chiao [Phys. Rev. Lett. 71, 708 (1993)]. The present model also leads to some predictions that can be tested experimentally.
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.
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.
Causal ``superluminal'' effects have recently been observed and discussed in various contexts. The question arises whether such effects could be observed with extremely weak pulses, and what would prevent the observation of an ``optical tachyon.'' Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett. 81, 2190 (1998)] have argued that quantum noise will preclude the observation of a superluminal group velocity when the pulse consists of one or a few photons. In this paper we reconsider this question both in a general framework and in the specific example, suggested by Chiao, Kozhekin, and Kurizki (CKK) [Phys. Rev. 77, 1254 (1996)], of off-resonant, short-pulse propagation in an optical amplifier. We derive in the case of the amplifier a signal-to-noise ratio that is consistent with the general ARS conclusions when we impose their criteria for distinguishing between superluminal propagation and propagation at the speed c. However, results consistent with the semiclassical arguments of CKK are obtained if weaker criteria are imposed, in which case the signal can exceed the noise without being ``exponentially large.'' We show that the quantum fluctuations of the field considered by ARS are closely related to superfluorescence noise. More generally, we consider the implications of unitarity for superluminal propagation and quantum noise and study, in addition to the complete and truncated wave packets considered by ARS, the residual wave packet formed by their difference. This leads to the conclusion that the noise is mostly luminal and delayed with respect to the superluminal signal. In the limit of a very weak incident signal pulse, the superluminal signal will be dominated by the noise part, and the signal-to-noise ratio will therefore be very small.
The mechanism of superluminal traversal time is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparison with a characteristic length of the incident wave packet, the reshaped wave packet with superluminal traversal time in transmission maintains the pro. le of the incident wave packet. In the case of potential barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier thickness dependence of the traversal time for thin barriers and its barrier thickness independence for thick barriers. This manifests the nature of the Hartman effect. Copyright (c) EPLA, 2008.
We identify the universal mechanism that is responsible for superluminal (faster-than-light) traversal times as well as the narrowing of wave packets transmitted through various nondissipative media. This mechanism is shown to be predominantly destructive interference between successive wave-packet components traversing all accessible causally retarded paths. It strongly depends on wave-packet coherence and width, and can cause superluminal traversal not only in evanescent-wave ``tunneling'' but also in allowed propagation. \textcopyright{} 1996 The American Physical Society.