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

Optics Express

Measuring optical tunneling times using a Hong-Ou-Mandel interferometer

D. J. Papoular, Pierre Cladé, Sergey Vladimirovich Polyakov, Colin F. McCormick, Alan L. Migdall, Paul D. Lett

Published Sep 24, 2008• 12 citations
Publisher

Abstract

We report a prediction for the delay measured in an optical tunneling experiment using Hong-Ou-Mandel (HOM) interference, taking into account the Goos-Hänchen shift generalized to frustrated total internal reflection situations. We precisely state assumptions under which the tunneling delay measured by an HOM interferometer can be calculated. We show that, under these assumptions, the measured delay is the group delay, and that it is apparently 'superluminal' for sufficiently thick air gaps. We also show how an HOM signal with multiple minima can be obtained, and that the shape of such a signal is not appreciably affected by the presence of the optical tunneling zone, thus ruling out the explanation of the anomalously short tunneling delays in terms of a reshaping of the wavepacket as it goes through the tunneling zone. Finally, we compare the predicted tunneling delay to a relevant classical delay and conclude that our predictions involve no non-causal effect.

DOI
10.1364/oe.16.016005

Related papers

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

ON SELECTING OPTIMAL PARAMETERS FOR DELAY TIME MEASUREMENT USING THE HONG–OU–MANDEL EFFECT

Dmitry Kuts, Mikhail S. Podoshvedov, А. Г. Воронцов +2 more

The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a HongOu-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.

Bulletin of the South Ural State University series Mathematics Mechanics Physics•Jan 1, 2025•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

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.

arXiv:quant-ph/9811019•Mysteries, Puzzles, and Paradoxes in Quantum Mechanics•Jan 1, 1999•3 citations

Simulating Quantum-Mechanical Barrier Tunneling Phenomena with a Nematic-Liquid-Crystal-Filled Double-Prism Structure

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

We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hänchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.

Molecular Crystals and Liquid Crystals•May 24, 2014•6 citations

Measurement of the single-photon tunneling time

Aephraim M. Steinberg, Paul G. Kwiat, R. Y. Chiao

Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.

Physical Review Letters•Aug 2, 1993•837 citations
We report a prediction for the delay measured in an optical tunneling experiment using Hong-Ou-Mandel (HOM) interference, taking into account the Goos-Hänchen shift generalized to frustrated total internal reflection situations. We precisely state assumptions under which the tunneling delay measured by an HOM interferometer can be calculated. We show that, under these assumptions, the measured delay is the group delay, and that it is apparently 'superluminal' for sufficiently thick air gaps. We also show how an HOM signal with multiple minima can be obtained, and that the shape of such a signal is not appreciably affected by the presence of the optical tunneling zone, thus ruling out the explanation of the anomalously short tunneling delays in terms of a reshaping of the wavepacket as it goes through the tunneling zone. Finally, we compare the predicted tunneling delay to a relevant classical delay and conclude that our predictions involve no non-causal effect.
The paper deals with the measurement error of the delay time between the arrivals at the beam splitter of two photons traveling through different channels in an optical system based on a HongOu-Mandel (HOM) interferometer. We consider the source of two-photon light to be the radiation of spontaneous parametric scattering (SPS) of light of the second type. The photon delay in one of the HOM interferometer channels can be induced by a change in the optical path length due to various factors: mechanical displacement of interferometer parts, changes in the refractive index of the medium caused by temperature variations, electric fields, etc. In the scheme, the outputs of the beam splitter are connected to single-photon detectors, which send signals to a coincidence counter upon photon detection. The coincidence counter data determine the delay time. The authors determine the absolute error in estimating the delay time in terms of the biphoton spectral width, the visibility, calculated from the maximum and minimum values of the coincidence counter signal, and the estimated delay time value itself. The derived expression facilitates finding the estimated delay time value. The study reveals that for a fixed biphoton field width, the delay time corresponding to the minimum absolute error value approaches the inflection point of the coincidence-time curve with decreasing visibility. This should be taken into account when designing measuring devices based on the Hong-Ou-Mandel interferometer.
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.
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.
We present an electrically-controlled nematic-liquid-crystal-filled double-prism structure that can be used to simulate quantum-mechanical tunneling through a barrier of variable height. Measurements of time delay in reflection from this structure, taken with femtosecond resolution using entangled photon pairs in a Hong-Ou-Mandel interferometer, are compared to theoretical predictions. We show that the Goos-Hänchen contribution to the tunneling delay is unmeasurable in this geometry. Our research contributes to the understanding of quantum-mechanical barrier tunneling times, and can lead to the fabrication of optical analogues to the tunnel junction and other photonic devices.
Using a two-photon interferometer, we have measured the time delay for a photon to tunnel across a barrier consisting of a 1.1-\ensuremath{\mu}m-thick 1D photonic band-gap material. The peak of the photon wave packet appears on the far side of the barrier 1.47\ifmmode\pm\else\textpm\fi{}0.21 fs earlier than it would if it were to travel at the vacuum speed of light c. Although the apparent tunneling velocity (1.7\ifmmode\pm\else\textpm\fi{}0.2)c is superluminal, this is not a genuine signal velocity, and Einstein causality is not violated. The measured tunneling time is consistent with the group delay (``phase time''), but not with the semiclassical time.