Related papers: Tunnelling Through Two Barriers
We study the tunneling through an arbitrary number of finite rectangular opaque barriers and generalize earlier results by showing that the total tunneling phase time depends neither on the barrier thickness nor on the inter-barrier…
We propose an analytical study of relativistic tunneling through opaque barriers. We obtain a closed formula for the phase time. This formula is in excellent agreement with the numerical simulations and corrects the standard formula…
Tunnelling transit time for a frustrated total internal reflection in a double-prism experiment was measured using microwave radiation. We have found that the transit time is of the same order of magnitude as the corresponding transit time…
In the case of tunneling of relativistic particles, differently from the nonrelativistic case, a limit of "transparent" barrier can also lead to an apparent "superluminal" behavior when considering the phase time. In this limit, the…
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…
With reference to a particle tunneling through two successive barriers, it seems to have been generally accepted that the tunneling time does not depend on the separation distance between the barriers. This phenomenon has been called the…
Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevence to the transmission of…
We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We…
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…
The tunneling time of particle through given barrier is commonly defined in terms of "internal clocks" which effectively measure the interaction time with internal degrees of freedom of the barrier. It is known that this definition of the…
We begin the Article with confusing citations in published papers on the question recently: how much time does a wave packet spend in a tunnelling barrier? ..a particle tunnelling through a barrier appears to do so in zero time 1. .. The…
Penetration of two coupled particles through a repulsive barrier is considered. A simple mechanism of the appearance of barrier resonances is demonstrated that makes the barrier anomalously transparent as compared to the probability of…
After a brief review of the derivation of the standard phase time formula, based on the use of the stationary phase method, we propose, in the opaque limit, an alternative method to calculate the phase time. The new formula for the phase…
We study the time required for a wave packet to tunnel beyond a square barrier, or to be reflected, by envisaging a physical clock which ticks only when the particle is within the barrier region. The clock consists in a magnetic moment…
Tunneling in the presence of an opaque barrier, part of which varies in time, is investigated numerically and analytically in one dimension. Clearly, due to the varying barrier a tunneling particle experiences spectral widening. However, in…
The celebrated Hartman effect, according to which, the tunneling time through a opaque barrier is independent of the width of the barrier for a sufficiently thick barrier, is not well understood theoretically and experimentally till today.…
Tunneling of optical pulses at 1.5 micron wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of…
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…
How much time does a tunneling wave packet spent in traversing a barrier? Quantum mechanical calculations result in zero time inside a barrier . In the nineties analogous tunneling experiments with microwaves were carried out. The results…
An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the…