Barrier Traversal Time Research Articles

First passage time of laser-driven tunneling.

The notion of the first passage time is shown to offer a meaningful extension to quantum tunneling, providing a closed-integral-form analytical unification of the tunneling rate and the tunneling passage time. We demonstrate that, in suitable potential settings, the quantum first passage time, found as a solution to the Fokker-Planck and backward Kolmogorov's equations for the quantum probability density, recovers the hallmark results for the Kramers escape rate, the lifetime of tunneling quasi-stationary wave packets, leads to a classical, distance-over-speed passage time for a free-particle wave function, and offers useful insights into Keldysh's intimation on the electron barrier-traversal time in field-induced ionization.

Instantaneous tunneling of relativistic massive spin-0 particles

The tunneling time problem studied earlier in Phys. Rev. Lett., 108 (2012) 170402, using a non-relativistic time-of-arrival (TOA) operator predicted that tunneling time is instantaneous. This raises the question whether instantaneous tunneling time is a consequence of using a non-relativistic theory. Here, we extend the analysis by proposing a formalism on the construction of relativistic TOA operators for spin-0 particles in the presence of an interaction potential V (q) via quantization. We then construct the corresponding barrier traversal time operator, and impose the condition that the barrier height V o is less than the rest mass energy of the particle. We show that only the above-barrier energy components of the incident wavepackets momentum distribution contribute to the barrier traversal time while the below-barrier components are transmitted instantaneously.

Quantum tunneling time: Insights from an exactly solvable model

Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can depart significantly from the scenario in which the barrier-traversal time is zero or very small. However, our findings do not support the idea of a well-defined tunneling time either. Our numerically exact results should help in finding a consensus about this fundamental problem.

Tunneling time in driven double‐well system using entangled molecular dynamics method

AbstractWe calculate quantum tunneling time in the double‐well system without perturbation and with symmetry‐breaking driven force using the entangled trajectory molecular dynamics method in the present article. Without perturbation, quantum tunneling time decreased with the increase of the energy, and the different contributions of the barrier traversal time and the intrinsic decay time have been shown. The tunneling time dependence on the amplitude and frequency of the symmetry‐breaking driven force are present. In the case of weak driven force, tunneling time has a minimum value in the resonant frequency. For strong driven force, chaos brings a huge change to quantum dynamics, tunneling time significantly becomes short. Finally, we directly show the enhancement of quantum tunneling process by chaotic behavior of entangled trajectories and indicate that it was caused by quantum effect.

Quantum traversal time through a double barrier

The generalized Hartmann effect (GHE) predicts a strict inequality between the traversal times across a contiguous and a separated double-barrier system. This is compared to the implications of the time-of-arrival (TOA) operator approach to barrier traversal time [E. A. Galapon, Phys. Rev. Lett. 108, 170402 (2012)]. It is shown that, for initial wave packets with compact supports in the far incident side of the barrier system, the expectation value of the traversal time is independent of the separation between the barriers. On the other hand, for wave packets with supports extending inside the first barrier, the contribution of the barrier separation to the traversal time exponentially increases with the barrier height. Our result shows that if the support of the incident wave packet is far from the barrier region, the GHE inequality is violated. However, if the support of the wave packet extends inside the barrier region, the GHE inequality is consistent with the TOA operator approach, but only when the particle's incident energy is very small.

Only Above Barrier Energy Components Contribute to Barrier Traversal Time

A time of arrival operator across a square potential barrier is constructed. The expectation value of the barrier time of arrival operator for a sufficiently localized incident wave packet is compared with the expectation value of the free particle time of arrival operator for the same wave packet. The comparison yields an expression for the expected traversal time across the barrier. It is shown that only the above barrier components of the momentum distribution of the incident wave packet contribute to the barrier traversal time, implying that below the barrier components are transmitted without delay. This is consistent with the recent experiment in attosecond ionization in helium indicating that there is no real tunneling delay time [P. Eckle et al., Science 322, 1525 (2008)].

Photonic tunneling time in frustrated total internal reflection

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.

Propagation features of evanescent acoustic waves

Evanescent waves are not true propagating waves, so questions regarding their traversal time or propagation direction are ill posed. However, physical phenomena related to the time delay of pulsed evanescent perturbations, or refraction effects through a discontinuity, can be easily put into evidence in acoustics by proper choice of acoustic modes and geometrical configuration. In this paper, lateral displacement and time delay through forbidden barriers of Lamb mode waves with contradirected phase and group velocities are studied. Low noise detection achieved by cutting off spurious mode generation and a common objection made toward experiments of this type is avoided. This objection states that the highest frequency components of the pulse travel faster and are less attenuated than the main carrier frequency of the packet, distorting the original pulse to such an extent as to render measurements unrelated to barrier traversal times. Elastic waves generated with piezoelectric transducers are injected into aluminum plates through wedge-shaped Lucite waveguides so as to generate the appropriate Lamb mode which traverses a forbidden region and is picked up after it with a similar setup of transducer and waveguide. Various configurations of wave barriers have been measured and possible theoretical interpretation is given.

Simulations of barrier traversal and reflection times based on event enhanced quantum theory

The formalism of event enhanced quantum theory is used to simulate traversal and reflection times of electrons through a one-dimensional barrier. The dependence of these times on the parameters of the barrier and the detectors is examined and the results are compared with those of selected approaches.

Barrier traversal times using a phenomenological track formation model

A phenomenological model for a measurement of “barrier traversal times” for particles is proposed. Two idealized detectors for passage and arrival provide entrance and exit times for the barrier traversal. The averaged traversal time is computed over the ensemble of particles detected twice, before and after the barrier. The “Hartman effect” can still be found when passage detectors that conserve the momentum distribution of the incident packet are used.

Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates.

Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. \textcopyright{} 1996 The American Physical Society.

Approaches to the tunneling time based on the Larmor clock and absorption probabilities as particular cases of the stay-time method.

The Larmor clock and the particle absorption approaches to the tunneling time are reexamined and extended to cover two- and three-dimensional systems and multichannel scattering. We show that both of them can be viewed as particular cases of the recent stay-time method. Furthermore, the barrier traversal time proposed by B\uttiker on the basis of the Larmor clock is found to correspond to the root-mean-square value of the actual tunneling time, rather than to the mean tunneling time.

Transfer-energy-dependent escape rate of electrons through a small-capacitance tunnel junction

The dynamics of a tunneling electron through a small-capacitance tunnel junction are studied by developing a method for self-consistently determining escape rate and barrier traversal time for those electrons that transfer a given energy to the electromagnetic environment. The transfer-energy-dependent escape rate lets us examine dissipative and nondissipative tunneling rates separately and its integral over the transfer energy gives the total escape rate that is obtained by the instanton technique. It is found that the escape rate increases exponentially with increasing the ratio of the elementary charging energy to the quantized energy of the environment, but that the traversal time peaks at one particular ratio. As the frequency of the electromagnetic mode increases, an effective potential is shown to change from linear (dominated by the zero-point fluctuations of charge on the junction) to parabolic (dominated by the static polarization of the charge). Possible experimental situations for observing the predicted effects are discussed.

Electron escape rate and barrier traversal time influenced by the electromagnetic environment.

Self-consistent determination of electron escape rate and barrier traversal time under the influence of the electromagnetic environment reveals that the escape rate increases monotonically with increasing ratio of the elementary charging energy to the barrier height but that the traversal time peaks at one certain ratio. As the freuqency of the electromagnetic mode increases, an effective potential for a tunneling electron changes from linear to parabolic, dominated, respectively, by the zero-point fluctuations of the charge on the junction and its static polarization. Possible experimental situations for observing these predictions are discussed.

Effects of barrier traversal time on escape rate through a small-capacitance tunnel junction

This paper describes self-consistent determination of the transfer-energy-dependent escape rate and barrier traversal time of electrons under the influence of the electromagnetic environment. This rate lets us examine dissipative and nondissipative tunneling rate separately and its integral over the transfer energy gives the total escape rate that is obtained by the instanton technique. It is found that the escape rate is exponentially enhanced as the capacitance of the junction is reduced.

Distribution of times for barrier traversal caused by energy fluctuations

Quantum tunneling is attributed to energy fluctuations permitted by the uncertainty principle. The distribution of barrier traversal times is shown to be bimodal. The expression for the expectation value is similar to the semiclassical result, and the width of the distribution varies inversely with the size of the barrier.

Limitations on the use of Bohm's causal interpretation of quantum mechanics for the computation of tunneling times

Others have used Bohm's causal interpretation to calculate barrier traversal times for plane waves and wavepackets. It is shown that Bohm's stream velocity does not represent the motion of any part when there is a superposition of waves. Calculated plane traversal times are upper bounds, and other difficulties are encountered using wavepackets.

Experiments pursuant to determining the barrier traversal time for quantum tunneling

Laser illumination of the junction of a scanning tunneling microscope (STM) modulates the barrier height by adding the electric field of light. Numerical simulations suggest that the dependence of tunneling current on the magnitude and frequency of the modulation can serve as a basis for determining the duration of barrier traversal. Modulation increases the mean value of the current when the frequency is much less than the reciprocal of the traversal time. Our simulations also suggest that a 670 nm laser diode at a power density of 100 W/cm2 will reduce the tunneling current. The latter effect is contrary to most competing phenomena such as current rectification, photo-assisted tunneling, thermal-assisted tunneling, and thermal expansion. We are completing a novel STM which has decreased noise and increased stability in order to make the laser/STM measurements. © 1993 John Wiley & Sons, Inc.

Determination of barrier traversal time by modulation of the incident wave

The semiclassical expression for barrier traversal time results from a variety of theoretical procedures, but it appears that an opaque barrier is required in each derivation. Following Büttiker and Landauer [IBM J. Res. Dev. 30, 451 (1986)], we use two interfering plane waves as the incident wave and determine the traversal time by attributing differences in the transmitted and incident waves to the ratio of dispersion in the transit time to the modulation period. Calculations are made for rectangular barriers with different sizes. There is essentially agreement with Büttiker and Landauer for opaque barriers which they considered, but the present solution does not diverge for energies near the top of the barrier.

On superluminal barrier traversal

We report on microwave measurements of barrier traversal time of electromagnetic wave packets in an undersized waveguide. This time was significantly shorter than the ratio L/c, with L the barrier length and c the velocity of light in vacuum. Consequently the transport velocity for the wave packet inside the barrier has to be superluminal, i.e. larger than c.