Tunneling of the wave packets having rectangular and Gaussian forms through a quantum diode is investigated. By using the potential of the system the S-matrix for this structure is obtained and the analytic expressions describing the form of the transmitted pulse are calculated. These analytic solutions are compared with the numeric ones. An excellent coincidence is detected. The time-delay for the Gaussian pulse tunneling through the quantum dot is investigated in details.

Jan 1, 20120 citations

Pulse normalization in slow-light media

B. Macke, Bernard Ségard

arXiv:physics/0601046Physical Review AApr 5, 200614 citations

arXiv:cond-mat/0409396 · Physical Review B

Pulse propagation in resonant tunneling

Ulrich Wulf, V. V. Skalozub

Published Oct 20, 2005• 11 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.72.165331

Related papers

Pulse Propagation in Resonant Tunneling II

Ulrich Wulf, V. V. Skalozub

We consider the analytically solvable model of a Gaussian pulse tunneling through a transmission resonance with a general Fano characteristic. It is demonstrated that the transmitted pulse contains enough information to determine uniquely all parameters defining the Fano resonance. This is in contrast to the measurement of the static conductance. Our analytical model is in agreement with numerical data published recently for the limit of a Breit-Wigner resonance. We identify two opposite pulse propagation regimes: if the resonance is broad compared to the energetic width of the incident Gaussian pulse a weakly deformed and slightly delayed transmitted Gaussian pulse is found. In the opposite limit of a narrow resonance the dying out of the transmitted pulse is dominated by the slow exponential decay characteristic of a quasi-bound state with a long life time. In this regime we find characteristic interference oscillations.We consider the analytically solvable model of a Gaussian pulse tunneling through a transmission resonance with a general Fano characteristic. It is demonstrated that the transmitted pulse contains enough information to determine uniquely all parameters defining the Fano resonance. This is in contrast to the measurement of the static conductance. Our analytical model is in agreement with numerical data published recently for the limit of a Breit-Wigner resonance. We identify two opposite pulse propagation regimes: if the resonance is broad compared to the energetic width of the incident Gaussian pulse a weakly deformed and slightly delayed transmitted Gaussian pulse is found. In the opposite limit of a narrow resonance the dying out of the transmitted pulse is dominated by the slow exponential decay characteristic of a quasi-bound state with a long life time. In this regime we find characteristic interference oscillations.

arXiv:cond-mat/0502286Feb 11, 20050 citations

Multiple Fano Resonances in Dynamic Resonant Tunneling Processes

Gilad Zangwill, Er’el Granot

The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.

Applied SciencesJun 2, 20232 citations

Tunneling of wave packages through resonant quantum systems

N. A. Ivanov, Natalia Yu. Filonenko

Tunneling of wave packages through resonant quantum systems presented in an S-matrix form is investigated. An arbitrary incident wave package can be written as the superposition of the Gaussian-form pulses and for latter ones the exact analytic solution was obtained already. As a practically interesting case, the transition of the rectangular wave package through the one-resonant level system is considered. Using developed recently modified saddle-points method the time-delay (Δt) of the wave pulses having Gaussian and rectangular form transmitted through a quantum system with resonance level is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependency Δt from width and energy of resonance levels, and the momentum of incident wave-package are illustrated. The results are compared with the ones obtained for tunneling of the one Gaussian package. Possible applications are discussed.Tunneling of wave packages through resonant quantum systems presented in an S-matrix form is investigated. An arbitrary incident wave package can be written as the superposition of the Gaussian-form pulses and for latter ones the exact analytic solution was obtained already. As a practically interesting case, the transition of the rectangular wave package through the one-resonant level system is considered. Using developed recently modified saddle-points method the time-delay (Δt) of the wave pulses having Gaussian and rectangular form transmitted through a quantum system with resonance level is investigated. The time delay, argument and amplitude of the outgoing wave are calculated. The dependency Δt from width and energy of resonance levels, and the momentum of incident wave-package are illustrated. The results are compared with the ones obtained for tunneling of the one Gaussian package. Possible applications are discussed.

IEEE International Conference Nanomaterials: Applications & Properties (NAP)Sep 1, 20170 citations

Exponential and nonexponential buildup in resonant tunneling

Roberto Romo, Alberto Hernández-Maldonado, Jorge Villavicencio

The exponential and nonexponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schr\"odinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a nonexponential regime. The buildup of the probability amplitude in the nonexponential regime follows a ${t}^{\ensuremath{-}3/2}$ time dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, $E={\ensuremath{\varepsilon}}_{n}$ with $n>1$ , it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from $n$ to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy $E$ .The exponential and nonexponential regimes of the buildup process in resonant tunneling structures are analyzed by considering an analytic solution of the time-dependent Schr\"odinger equation. It is found that the buildup exhibits a purely exponential behavior in a finite time interval followed by a clear transition to a nonexponential regime. The buildup of the probability amplitude in the nonexponential regime follows a ${t}^{\ensuremath{-}3/2}$ time dependence, in the same fashion as the survival amplitude in quantum decay. For incidence energies at higher isolated resonances, $E={\ensuremath{\varepsilon}}_{n}$ with $n>1$, it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from $n$ to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy $E$.

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Transmission of wave packets through open mesoscopic systems

N. A. Ivanov, V. V. Skalozub

Jan 1, 20120 citations

Pulse normalization in slow-light media

B. Macke, Bernard Ségard

We analytically study the linear propagation of arbitrarily shaped light pulses through an absorbing medium with a narrow transparency window or through a resonant amplifying medium. We point out that, under certain general conditions, the pulse acquires a nearly Gaussian shape, irrespective of its initial shape and of the spectral profile of the line. We explicitly derive in this case the pulse parameters, including its skewness, responsible for a deviation of the delay of the pulse maximum from the group delay. We illustrate our general results by analyzing the slow-light experiments having demonstrated the largest fractional pulse delays.We analytically study the linear propagation of arbitrarily shaped light pulses through an absorbing medium with a narrow transparency window or through a resonant amplifying medium. We point out that, under certain general conditions, the pulse acquires a nearly Gaussian shape, irrespective of its initial shape and of the spectral profile of the line. We explicitly derive in this case the pulse parameters, including its skewness, responsible for a deviation of the delay of the pulse maximum from the group delay. We illustrate our general results by analyzing the slow-light experiments having demonstrated the largest fractional pulse delays.

arXiv:physics/0601046Physical Review AApr 5, 200614 citations

n>1

, it is found that the exponential regime is split into two exponential subregimes: the first one is governed by the width ${\ensuremath{\Gamma}}_{n}$ of the resonance chosen for the incidence energy, and the second one is dominated by the width ${\ensuremath{\Gamma}}_{1}$ of the lowest resonance. The transition occurs directly from

n

to 1 without jumps to other intermediate resonant states. This dynamics is discussed in comparison with the (opposite) and well-studied process of quantum decay, with which we find that there are striking similarities in both the exponential and nonexponential regimes. We also analyze the buildup in systems with resonance doublets, where the interference effects produced by the interacting resonances play an important role. In the latter case we find that the buildup of the probability amplitude exhibits a complex oscillatory behavior that can be characterized by a mix of oscillating contributions with well-defined Rabi type frequencies of the form $|E\ensuremath{-}{\ensuremath{\varepsilon}}_{n}|/\ensuremath{\hbar}$, where ${\ensuremath{\varepsilon}}_{n}$ are the nearest resonances around the incidence energy

E