Tunneling by an electron packet with an initially sharp wavefront

Teranishi, Nobukazu; Kriman, A. M.; Ferry, D. K.

doi:10.1016/0749-6036(87)90233-3

Cited by 35 publications

(22 citation statements)

References 10 publications

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“…Other works had already pointed out the dominance of non-tunneling components in the forerunner [218,219,171,59,60] but had not characterized its time dependence.…”

Section: Muga-büttiker Analysis Of Evanescent Wavesmentioning

confidence: 98%

Quantum transients

2009

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Quantum transients are temporary features of matter waves before they reach a stationary regime. Transients may arise after the preparation of an unstable initial state or due to a sudden interaction or a change in the boundary conditions. Examples are diffraction in time, buildup processes, decay, trapping, forerunners or pulse formation, as well as other phenomena recently discovered, such as the simultaneous arrival of a wave peak at arbitrarily distant observers. The interest on these transients is nowadays enhanced by new technological possibilities to control, manipulate and measure matter waves.Comment: review article, 76 pp, 36 figures, more content, typos correcte

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“…Other works had already pointed out the dominance of non-tunneling components in the forerunner [218,219,171,59,60] but had not characterized its time dependence.…”

Section: Muga-büttiker Analysis Of Evanescent Wavesmentioning

confidence: 98%

Quantum transients

2009

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“…But later, more accurate studies of the punctual source problem or other boundary conditions showed that the contribution from the saddle point (due to to frequency components above or at the frequency cutoff created by the sharp onset of the source emission), and possibly from other critical points (e.g. resonance poles when a square barrier is located in front of the source [12]) were generally dominant at τ , so that no sign of the ω 0 −front (4) can in fact be seen in the total wave density at that time [8][9][10][11][12]. Similarly, corrections to the original work by Sommerfeld and Brillouin have been also worked out for electromagnetic pulse propagation [13].…”

Section: Introductionmentioning

confidence: 99%

Time dependence of evanescent quantum waves

Muga

Büttiker

2000

Phys. Rev. A

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The time dependence of quantum evanescent waves generated by a point source with an infinite or a limited frequency band is analyzed. The evanescent wave is characterized by a forerunner (transient) related to the precise way the source is switched on. It is followed by an asymptotic, monochromatic wave which at long times reveals the oscillation frequency of the source. For a source with a sharp onset the forerunner is exponentially larger than the monochromatic solution and a transition from the transient regime to the asymtotic regime occurs only at asymptotically large times. In this case, the traversal time for tunneling plays already a role only in the transient regime. To enhance the monochromatic solution compared to the forerunner we investigate (a) frequency band limited sources and (b) the short time Fourier analysis (the spectrogram) corresponding to a detector which is frequency band limited. Neither of these two methods leads to a precise determination of the traversal time. However, if they are limited to determine the traversal time only with a precision of the traversal time itself both methods are successful: In this case the transient behavior of the evanescent waves is at a time of the order of the traversal time followed by a monochromatic wave which reveals the frequency of the source.Comment: 16 text pages and 9 postscript figure

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“…This is the case of the point source initial condition problem that * Electronic address: villavics@uabc.edu.mx has been of great interest since the original proposal by Stevens [12] of tunneling monochromatic fronts. Aside from the controversy regarding the propagation of such tunneling wavefronts [13][14][15], the issue was later investigated in Refs. 16 and 17, that showed the existence of non-tunneling forerunners in evanescent media, with the interesting result that the time of arrival of these transient structures is governed by the traversal or Büttiker-Landauer time [18].…”

Section: Introductionmentioning

confidence: 99%

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

Nieto-Guadarrama

Villavicencio

2020

Phys. Rev. A

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We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point source initial condition. We show that in both the propagation, and Klein-tunneling regimes, the Zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the Zitterbewegung frequency, and that the amplitude of these oscillations decays as t −3/2 . We show that beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cut-off quantum states. We also find a time-domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction in time phenomenon observed in non-relativistic systems. The relative positions of these wavefronts are used to investigate the time-delay of quantum waves in the Klein-tunneling regime. We show that, depending on the energy difference, E, between the source and the potential step, the time-delay can be positive, negative or zero. The latter case corresponds to a super-Klein-tunneling configuration, where E equals to half the energy of the potential step.

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Tunneling by an electron packet with an initially sharp wavefront

Cited by 35 publications

References 10 publications

Quantum transients

Quantum transients

Time dependence of evanescent quantum waves

Zitterbewegung and Klein-tunneling phenomena for transient quantum waves

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