On the concept of the tunneling time

How much time does a wave packet spent in tunneling a barrier? Quantum mechanical calculations result in zero time inside a barrier. In the nineties analogous tunneling experiments with microwaves were carried out confirming quantum mechanics. Electron tunneling time is hard to measure being extremely short. However, quite recently the atomic ionization tunneling time has been measured. Experimental data of photonic, phononic, and electronic tunneling time is available now. I...

A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model I employ has the advantage of yielding sensible results for energy eigenstates, and does not require the use of time-dependant wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not...

In the B\"uttiker-Landauer perturbation approach to electron tunnelling, through a time-modulated rectilinear potential barrier, the Tien-Gordon identity was invoked, together with its infinite energy spectrum. Here, an exact treatment is presented which is based on the temporal wave-function matching procedure, that led to a finite energy spectrum. In seeking the condition governing the time evolution of the tunnelling process, the Euler formula provided the crucial ingredie...

We study the tunneling zone solutions of a one-dimensional electrostatic potential for the relativistic (Dirac to Klein-Gordon) wave equation when the incoming wave packet exhibits the possibility of being almost totally transmitted through the barrier. The transmission probabilities, the phase times and the dwell times for the proposed relativistic dynamics are obtained and the conditions for the occurrence of accelerated tunneling transmission are all quantified. We show th...

Exact analytical solutions of the time-dependent Schr\"odinger equation with the initial condition of an incident cutoff wave are used to investigate the traversal time for tunneling. The probability density starts from a vanishing value along the tunneling and transmitted regions of the potential. At the barrier width it exhibits, at early times, a distribution of traversal times that typically has a peak $\tau_p$ and a width $\Delta \tau$. Numerical results for other tunnel...

We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full-tunneling...

As was shown in quant-ph/0405028, the state of a tunneling particle can be uniquely presented as a coherent superposition of two states to describe alternative sub-processes, transmission and reflection. In this paper, on the basis of the stationary wave functions for these sub-processes, we give new definitions of the dwell times for transmission and reflection. In the case of rectangular potential barriers the dwell times are obtained explicitly. In contrast with the well-k...

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 pulse transit through the barrier itself seems to be instantaneous 2. ..tunnelling is unlike to be an instantaneous process 3. ..ionization time is close to zero 4. ..all waves have a zero tunneling time [5]. ..Our results are inconsistent wi...

The quantum shutter approach to tunneling time scales (G. Garc\'{\i }a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which uses a cutoff plane wave as the initial condition, is extended in such a way that a certain type of wave packet can be used as the initial condition. An analytical expression for the time evolved wave function is derived. The time-domain resonance, the peaked structure of the probability density (as the function of time) at the exit o...

In this paper we compare the concept of the tunneling time introduced in quant-ph/0405028 with those of the phase and dwell times. As is shown, unlike the latter our definition of the transmission time coincides, in the limit of weak scattering potentials, with that for a free particle. This is valid for all values of the particle's momentum, including the case of however slow particles. All three times are also considered for a resonant tunneling. In all the cases the main f...