General way to define tunneling time

With the development of attosecond science, tunneling time can now be measured experimentally with the attoclock technique. However, there are many different theoretical definitions of tunneling time and no consensus has been achieved.Here, we bridge the relationship between different definitions of tunneling time based on a quantum travel time in onedimensional rectangular barrier tunneling problem. We find that the real quantum travel time t_(Re) is equal to the Bohmian time t_(Bohmian), which is related to the resonance lifetime of a bound state. The total quantum travel time τt can perfectly retrieve the transversal time t_x and the Büttiker–Landauer time τ_(BL) in two opposite limits, regardless of the particle energy.     

Delay time computation for relativistic tunneling particles

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 that, in some limiting cases, the analytical difficulties that arise when the stationary phase method is employed for obtaining phase (traversal) tunneling times are all overcome. Lessons concerning the phenomenology of the relativistic tunneling suggest revealing insights into condensed-matter experiments using electrostatic barriers for which the accelerated tunneling effect can be observed. PACS 03.65.Xp     

Interference and dispersion effects on tunneling time

We study the interplay between pulse width, interference and tunneling for a wave packet incident upon a barrier and, within the context of tunneling time, we offer a complementary insight into the origin of the Hartman effect. We find that interference together with momentum spread lower (increase) the transmission (reflection) tunneling time thereby `breaking the symmetry between transmission and reflection times'. But, within the limits of our method, we are unable to confirm that negative tunneling time can be obtained.     

Closed formulas for tunneling time in superlattices

New formulas for an exact and simple evaluation of the phase time associated with the passage of electrons or photons through a finite superlattice are derived. This time, named here the superlattice-tunneling time tau(n), exhibits a resonant-band structure or a superluminal phase time behavior depending on whether the particle's energy lies in a band or a gap. In the band, tau(n) remains larger than the free motion time tau(f), while in the gap it can be less than tau(f) (with strong substrate effects), but it is larger than the single-cell phase time tau(1). Extremely good agreements with optical-pulse and superluminal delay times measured by Spielmann et al. and Steinberg et al. are found, including the superlattice-tunneling-time limit and the substrate effects. Conditions for measurements of earlier electron arrival are also analyzed.     

Experimental analysis of resonant tunneling transit time using high-frequency characteristics of resonant tunneling transistors

We systematically estimate the resonant tunneling transit time from the high-frequency characteristics of resonant tunneling transistors. It is found that the transit time across an InGaAs/InAlAs resonant tunneling structure is more than one order of magnitude shorter than that for GaAs/AlAs with the same barrier layer thickness. In addition, the obtained times agree reasonably well with calculated phase time. It is probably the elastic resonance width and not the inelastic scattering effect that mainly determines the resonant tunneling transit time.     

Phase time in Kane type barrier tunneling

The behavior of Wigner phase delay time in the reflection mode is studied taking into account the real band structure of Kane type semiconductor quantum ring. It's calculated the analytical expression for the saturated delay time. It's shown that the saturated delay time is independent of the width of the opaque barrier.     

A note on the tunneling time problem

A remarkable feature of barrier penetration in quantum theory is that a particle tunneling through a barrier appears to do so in zero time. We analyze the conditions that would make possible an actual measurement of an anomalously short traversal time and conclude that such a measurement cannot be made.     

A note on traversal time for tunneling

A simple approach to study the traversal time for tunneling is given. By using the WKB wave function to evaluate the velocity field of particles in the barrier region, an expression for the traversal time τ=εdx[m/2(V(x)-E)]^1/2 is obtained in conformity with the recent results.     

Causality and time dependence in quantum tunneling

Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the presence of a positive potential no part of the distribution is transported faster than the free particle. For the case of a small initial momentum uncertainty, the deformation of the coordinate density is considered, including a possible advance of its maximum, which would not mean any noncausal signal transport. Supported by G. I. F.     

黑洞量子隧穿过程的时间

讨论了弯曲时空中黑洞量子隧穿的时间.在假定了黑洞量子隧穿是一个瞬时过程的情况下,通过利用WKB法得出了有静止质量粒子的量子隧穿辐射谱.该辐射谱表明对于在黑洞视界处有静止质量粒子的出射也满足量子力学中的幺正性原理,支持Parikh-Wilczek的结论.结果的合理性表明,在黑洞视界处的量子隧穿过程可以看成是一个瞬时过程.     

On the tunneling through a time dependent barrier

Tunneling of a nucleon through a monotonically shrinking rectangular barrier is solved exactly. Some consequences for the nucleon-transfer in the approach phase of two colliding heavy nuclei are discussed.     

Electron tunneling through a barrier that depends linearly on time

We discuss the creation of a negative molecular ion via the decay of a self-captured electron state — the fluctuon — in a nonideal dipole-molecule gas. The creation probability of the negative ion is evaluated in the classical approximation using Green's function methods. We assume that the potential barrier through which the electron tunnels from the potential well of the fluctuon to that of the molecule depends linearly on time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 84–88, September, 1987.     

The asymmetry of the tunneling time in type II semiconductor heterostructures

The tunneling time asymmetry in type II semiconductor heterostructures is related to the phase difference of the reflection coefficients for the two tunneling directions. Analytical expressions and numerical simulations are given for the difference between the left-to-right and right-to-left tunneling times in asymmetric, single and multiple barrier type II heterostructures.     

A green function approach to the relaxation time of phonon assisted tunneling

Although many elegant formulations of the phonon assisted tunneling problem have been given, the calculation of the relaxation time itself always has been based on the “golden rule”, which requires the artifice of a fictitious static field. In this communication the relaxation time is given by means of linear response theory, unitary transformations and an application of the Bogoliubov inequality. The artifice of a static field is no longer required.     

Rashba spin-orbit effect on dwell time of electrons tunneling through semiconductor barrier

A study on characteristics of electrons tunneling through semiconductor barrier is evaluated, in which we take into account the effects of Rashba spin-orbit interaction. Our numerical results show that Rashba spin-orbit effect originating from the inversion asymmetry can give rise to the spin polarization. The spin polarization does not increase linearly but shows obvious resonant features as the strength of Rashba spin-orbit coupling increases, and the amplitudes of spin polarization can reach the highest around the first resonant energy level. Furthermore, it is found that electrons with different spin orientations will spend quite different time through the same heterostructures. The difference of the dwell time between spin-up and spin-down electrons arise from the Rashba spin-orbit coupling. And it is also found that the dwell time will reach its maximum at the first resonant energy level. It can be concluded that, in the time domain, the tunneling processes of the spin-up and spin-down electrons can be separated by modulating the strength of Rashba spin-orbit coupling. Study results indicate that Rashba spin-orbit effect can cause a nature spin filter mechanism in the time domain.     

On the tunneling time of arbitrary continuous potentials and the Hartman effect

This paper obtains a generalized tunneling time of one-dimensional potentials via time reversal invariance.It also proposes a simple explanation for the Hartman effect using the useful concept of the scattered subwaves.