Average transmission times for the tunneling of wave packets

Lunardi, José T.; Manzoni, Luiz A.; Nystrom, Andrew T.; Perreault, Brent

doi:10.1007/s10946-011-9232-0

Cited by 3 publications

(4 citation statements)

References 25 publications

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“…The top plot of Figure 6 shows that for the less opaque barrier there exists a (very small) probability to observe a superluminal tunneling time. Even if this possibility cannot be precluded in principle, (see, e.g., [16]), in the present case the possibility of emergence of such small times was expected, since at t = 0 there was a significant portion of the wave packet (roughly 27%) penetrating the whole distance of the barrier, and this has an important contribution to the emergence of small times in the clock's readings associated to the transmitted particle. On the other hand, the top plot of Figure 7 shows that for the thicker barrier the probability for superluminal times is negligible -the portion of the wave packet already inside the barrier at t = 0 is the same (∼ 27%), but the wave packet penetrates proportionally a smaller distance inside the barrier and, thus, it does not contribute in a significant way to the emergence of very small times in the clock readings.…”

Section: ∂ω ∂Qmentioning

confidence: 58%

“…Still, the intrinsic experimental difficulties associated both with the measurements and the interpretation of the results have, so far, prevented an elucidation of the problem and, in fact, contradictory results persist, with some experiments obtaining a finite non-zero result [3,6] and others compatible with instantaneous tunneling [4]. It should be noticed that the similarity between Schrödinger and Helmholtz equations allows for analogies between quantum tunneling of massive particles and photons [7], and a noninstantaneous tunneling time is supported by this analogy and experiments measuring photonic tunneling times [8], as well as by many theoretical calculations based on both the Schrödinger (for reviews see, e.g., [1,2]) and the Dirac equations (e.g., [9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

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A Probability Distribution for Quantum Tunneling Times

Lunardi

Manzoni

2018

Advances in High Energy Physics

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We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.

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Section: ∂ω ∂Qmentioning

confidence: 58%

Section: Introductionmentioning

confidence: 99%

A Probability Distribution for Quantum Tunneling Times

Lunardi

Manzoni

2018

Advances in High Energy Physics

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“…It was shown that, for wave packets of finite width, such average transmission time does not saturate in the limit of opaque barriers for symmetric potentials, which is an important result associated with the Hartman effect [15]. One must notice, however, that the absence of saturation is not enough to prevent apparent superluminal speeds in the relativistic case [29] but, as pointed by Davies [30], the SWP clock times can be interpreted as weak values [31,32], and such results are not unexpected for weak values when they are associated with small probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…The results in [28,29] were obtained considering symmetric potentials, in which case the average transmission (reflection) SWP times coincide with the average of the dwell time over the transmitted (reflected) sub-ensemble [28] (as a consequence of the identity between the stationary SWP and dwell times for such potentials). Therefore, in order to better understand the properties of the average SWP clock times introduced in [28], it is necessary to analyze a situation in which they differ from the dwell time averaged over the corresponding sub-ensemble, such as for asymmetric potentials.…”

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confidence: 98%

Average clock times for scattering through asymmetric barriers

2014

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The reflection and transmission Salecker-Wigner-Peres clock times averaged over the postselected reflected and transmitted sub-ensembles, respectively, are investigated for the one dimensional scattering of a localized wave packet through an asymmetric barrier. The dwell time averaged over the same post-selected sub-ensembles is also considered. The emergence of negative average reflection times is examined and we show that while the average over the reflected sub-ensemble eliminates the negative peaks at resonance for the clock time, it still allows negative values for transparent barriers. The saturation of the average times with the barrier width (Hartman effect) is also addressed.PACS. 03.65.Xp Tunneling, traversal time, quantum Zeno dynamics -03.65.Ta Foundations of quantum mechanics; measurement theory -03.65.Nk Scattering theory IntroductionThe search for a sensible definition of quantum tunneling times is one of the most enduring problems in quantum mechanics, despite numerous efforts in the last few decades (see, e.g., [1,2,3,4,5,6,7,8,9,10] and references therein). The difficulty in obtaining a time scale for the tunneling problem lies in the well-known impossibility of defining a selfadjoint time operator canonically conjugated to the (bounded from below) Hamiltonian. Attempts to use a "tempus" operator that is canonically conjugated to the Hamiltonian but not given by the time evolution of the system, have lead to complex stationary times [11,12] (also see [13] for a review of methods attempting to define time operators).A more common approach to this problem is to obtain operational definitions of a parameter with the dimensions of time and investigate its properties. These attempts have rendered several definitions of time that, while useful in specific situations, are generally not considered the definitive answer to the question of how long it takes for a particle to tunnel through a potential barrier. Among the most common (and useful) stationary time scales considered in the literature are the much studied phase time [14,15], dwell time [16,17], Larmor time [17,18,19] (also see [20,21]) and the Salecker-Wigner-Peres (SWP) clock times [22,23,24,25].Recently, the SWP clock has been reconsidered and it was shown that, contrary to previous claims in the literature, it can be directly applied to interacting particles (i.e., without the need for "calibration" [26,27]) provided that one follows Peres' [23] approach to associate the clock's hand with the peak of the clock's wave function [24]. In particular, this approach allowed the derivation, directly from Schrödinger's equation, of a relationship between the dwell time and the SWP clock reflection and transmission times without an interference term [24], thus ending the controversy about the compatibility of such relationship with standard quantum mechanics (see, e.g., [1,2,3,4] and references therein).The SWP clock has also been used to treat the scattering of a wave packet by a potential and to obtain, by making use of a post-selection of the fina...

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Thermal quantum transition-path-time distributions, time averages, and quantum tunneling times

Pollak

2017

Phys. Rev. A

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Average transmission times for the tunneling of wave packets

Cited by 3 publications

References 25 publications

A Probability Distribution for Quantum Tunneling Times

A Probability Distribution for Quantum Tunneling Times

Average clock times for scattering through asymmetric barriers

Thermal quantum transition-path-time distributions, time averages, and quantum tunneling times

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