The “Tunneling-Time Problem” for Electrons

C. Richard Leavens

Anthony D. Challinor, Anthony Norden Lasenby, Shyamal S. Somaroo +2 more

Igor A. Ivanov, Kyung Taec Kim

We report a study of the effect of relativity on the tunneling time for the process of the tunneling ionization. Our results indicate that the relativistic effects make the tunneling time nonzero. A time interval of a few attoseconds is required for the electron to traverse the barrier. This finding agrees with the basic postulate of the special relativity that two events which are in causal relationship cannot occur simultaneously.

N. Yamada

Daniel Bakucz Canário, Michael Klaiber, Karen Z. Hatsagortsyan +1 more

The problem of time delay in tunneling ionization is revisited. The origin of time delay at the tunnel exit is analyzed, underlining the two faces of the concept of the tunneling time delay: the time delay around the tunnel exit and the asymptotic time delay at a detector. We show that the former time delay, in the sense of a delay in the peak of the wave function, exists as a matter of principle and arises due to the sub-barrier interference of the reflected and transmitted components of the tunneling electronic wave packet. We exemplify this by describing the tunneling ionization of an electron bound by a short-range potential within the strong-field approximation in a ``deep tunneling'' regime. If sub-barrier reflections are extracted from this wave function, then the time delay of the peak is shown to vanish. Thus, we assert that the disturbance of the tunneling wave packet by the reflection from the surface of the barrier causes a time delay in the neighborhood of the tunnel exit.

Guowen Wang

There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of an electron tunneling through a rectangular barrier are numerically calculated. No superluminal effect (Hartman effect) is found for the tunneling electron. Heisenberg's energy-time uncertainty relation for the tunneling effect is verified by calculating an introduced coefficient representing uncertainty. The present author argues that phase time, dwell time and Bütticker-Landauer time are not appropriate expressions for the actual transit time in a tunneling process. A quantum high-jumping model is presented to resolve the paradox that kinetic energy of the tunneling particle is negative and its momentum is imaginary.