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 Letters

Dual Optical Tunneling Times in Frustrated Total Internal Reflection

Ph. Balcou, Laurent Dutriaux

Published Feb 3, 1997• 260 citations
Publisher

Abstract

We investigate experimentally the optical tunneling times associated with frustrated total internal reflection of a light beam. Using as physical clocks the lateral shifts and angular deviations suffered by the transmitted and reflected beams, we measure both components of a complex tunneling time: the phase time and a semiclassical time. The phase time is shown to imply superluminal velocities and to depend strongly on boundary conditions not linked to the tunneling process. By contrast, the semiclassical time yields subluminal velocities and is related solely to tunneling.

DOI
10.1103/physrevlett.78.851

Related papers

Photonic tunneling time in frustrated total internal reflection

A. A. Stahlhofen

Frustrated total internal reflection is considered as the classical analog of quantum-mechanical tunneling. Here the tunneling time in frustrated total internal reflection is discussed. It is shown that the phase time allows for vanishing and negative barrier traversal times. The tunneling time is shown to be dominated by a time scale based on the Goos-H\"anchen shift. The role of further nonspecular deformations of the transmitted beam is addressed. The resulting tunneling times are compared with experimental data.

Physical Review A•Jun 16, 2000•41 citations

TUNNELING TIME OF A PARTICLE: TWO-DIMENSIONAL APPROACH

Chang-Soo Park

A two-dimensional problem of tunneling of a particle is studied to propose an experiment to measure tunneling time. We consider a 2D rectangular barrier in which the particle undergoes both tunneling and free lateral motion at the same time. The two processes are coupled by the same tunneling time, which leads to a simple relation between the tunneling time and the corresponding lateral shift such that L = vτ. Since the lateral speed v is constant the tunneling time can be obtained by measuring the lateral shift. The shifted length can be controlled by an initial lateral speed and become over a hundred nanometers when the particle is provided with sufficient initial lateral speed. The present model may also be used for examining the relationships between characteristic tunneling times suggested in previous articles. We also demonstrate physical differences between the 2D problem of a particle tunneling and the frustrated total internal reflection of electromagnetic waves.

Modern Physics Letters B•Nov 9, 2007•1 citation

Superluminal energy and information transport?

A. A. Stahlhofen, H. Druxes

The widespread belief, that energy and signal velocities are bounded by the speed of light in vacuum has been challenged in recent years by observations of superluminal propagation of classical evanescent modes in tunneling time experiments. These experiments thus provide a frame for testing the limits of transport velocities physically achievable. Obvious and hidden time-scales involved in tunneling time experiments are discussed focussing on optical tunneling in frustrated total internal reflection. A suggestion for a direct test of the energy transport velocity—also of interest in future hyper-fast space travel—is presented. Related questions touching our current understanding of some fundamental concepts in physics are addressed.

AIP conference proceedings•Jan 1, 1999•0 citations

Time-Domain Measurements of Reflection Delay in Frustrated Total Internal Reflection

George M. Gehring, Andreas C. Liapis, Svetlana G. Lukishova +1 more

We present experimental evidence that the contribution of the Goos-Hänchen shift to tunneling delay is suppressed in frustrated total internal reflection. We use a Hong-Ou-Mandel interferometer to perform direct time measurements of reflection delays with femtosecond resolution at optical frequencies, and take advantage of a liquid-crystal-filled double-prism structure to dynamically change the refractive index of the barrier region.

Physical Review Letters•Jul 18, 2013•18 citations

A unified theory of tunneling times promoted by Ramsey clocks

Patrik Schach, Enno Giese

What time does a clock tell after quantum tunneling? Predictions and indirect measurements range from superluminal or instantaneous tunneling to finite durations, depending on the specific experiment and the precise definition of the elapsed time. Proposals and implementations use the atomic motion to define this delay, although the inherent quantum nature of atoms implies a delocalization and is in sharp contrast to classical trajectories. Here, we rely on an operational approach: We prepare atoms in a coherent superposition of internal states and study the time read-off via a Ramsey sequence after the tunneling process without the notion of classical trajectories or velocities. Our operational framework (i) unifies definitions of tunneling delay within one approach, (ii) connects the time to a frequency standard given by a conventional atomic clock that can be boosted by differential light shifts, and (iii) highlights that there exists no superluminal or instantaneous tunneling.

arXiv:2404.14382•Science Advances•Apr 17, 2024•4 citations

Tunneling time in the case of frustrated total reflection

Daniela Mugnai, Anedio Ranfagni, Laura Ronchi

The tunneling time is here investigated by means of an electromagnetic model, for a system where a gap, between two parallel planes, acts as a classically-forbidden region for an impinging pulse with incidence angle larger than the critical angle. In all cases of frustrated total reflection we obtain a superluminal behavior both for phase and group delays.

arXiv:physics/0111192•Nov 27, 2001•2 citations
We investigate experimentally the optical tunneling times associated with frustrated total internal reflection of a light beam. Using as physical clocks the lateral shifts and angular deviations suffered by the transmitted and reflected beams, we measure both components of a complex tunneling time: the phase time and a semiclassical time. The phase time is shown to imply superluminal velocities and to depend strongly on boundary conditions not linked to the tunneling process. By contrast, the semiclassical time yields subluminal velocities and is related solely to tunneling.
Frustrated total internal reflection is considered as the classical analog of quantum-mechanical tunneling. Here the tunneling time in frustrated total internal reflection is discussed. It is shown that the phase time allows for vanishing and negative barrier traversal times. The tunneling time is shown to be dominated by a time scale based on the Goos-H\"anchen shift. The role of further nonspecular deformations of the transmitted beam is addressed. The resulting tunneling times are compared with experimental data.
A two-dimensional problem of tunneling of a particle is studied to propose an experiment to measure tunneling time. We consider a 2D rectangular barrier in which the particle undergoes both tunneling and free lateral motion at the same time. The two processes are coupled by the same tunneling time, which leads to a simple relation between the tunneling time and the corresponding lateral shift such that L = vτ. Since the lateral speed v is constant the tunneling time can be obtained by measuring the lateral shift. The shifted length can be controlled by an initial lateral speed and become over a hundred nanometers when the particle is provided with sufficient initial lateral speed. The present model may also be used for examining the relationships between characteristic tunneling times suggested in previous articles. We also demonstrate physical differences between the 2D problem of a particle tunneling and the frustrated total internal reflection of electromagnetic waves.
The widespread belief, that energy and signal velocities are bounded by the speed of light in vacuum has been challenged in recent years by observations of superluminal propagation of classical evanescent modes in tunneling time experiments. These experiments thus provide a frame for testing the limits of transport velocities physically achievable. Obvious and hidden time-scales involved in tunneling time experiments are discussed focussing on optical tunneling in frustrated total internal reflection. A suggestion for a direct test of the energy transport velocity—also of interest in future hyper-fast space travel—is presented. Related questions touching our current understanding of some fundamental concepts in physics are addressed.
What time does a clock tell after quantum tunneling? Predictions and indirect measurements range from superluminal or instantaneous tunneling to finite durations, depending on the specific experiment and the precise definition of the elapsed time. Proposals and implementations use the atomic motion to define this delay, although the inherent quantum nature of atoms implies a delocalization and is in sharp contrast to classical trajectories. Here, we rely on an operational approach: We prepare atoms in a coherent superposition of internal states and study the time read-off via a Ramsey sequence after the tunneling process without the notion of classical trajectories or velocities. Our operational framework (i) unifies definitions of tunneling delay within one approach, (ii) connects the time to a frequency standard given by a conventional atomic clock that can be boosted by differential light shifts, and (iii) highlights that there exists no superluminal or instantaneous tunneling.