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Journal of Physics B Atomic Molecular and Optical Physics

Localization of energy exchanges in field-assisted double-barrier resonant tunnelling: II. The two-level case

C Pérez del Valle, R. Lefèbvre, Osman Atabek

Published Mar 14, 2001• 1 citation
Publisher

Abstract

We examine the transmissivity through a double-barrier potential with two resonances present in the intermediate well. The particle interacts with an oscillating field. Satellites are produced when the particle needs to emit or absorb one or more quanta of the field to reach the resonant energy which favours transmissivity. We show that as the frequency of the field goes from an off-resonance to the resonant situation, where there is matching with the energy separation of the well levels, the discontinuities responsible for the energy exchanges are first the most external ones, but finally the most internal ones. We also conclude that, even in the presence of an oscillating field, the propagation within the barriers is well accounted for by free waves.

DOI
10.1088/0953-4075/34/6/310

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We examine the transmissivity through a double-barrier potential with two resonances present in the intermediate well. The particle interacts with an oscillating field. Satellites are produced when the particle needs to emit or absorb one or more quanta of the field to reach the resonant energy which favours transmissivity. We show that as the frequency of the field goes from an off-resonance to the resonant situation, where there is matching with the energy separation of the well levels, the discontinuities responsible for the energy exchanges are first the most external ones, but finally the most internal ones. We also conclude that, even in the presence of an oscillating field, the propagation within the barriers is well accounted for by free waves.
A transfer-matrix technique is formulated to treat the scattering of a particle incident on a piecewise constant potential and interacting with an oscillatory field. A study of tunneling through a single barrier shows in the transmission probabilities, for absorption or emission of quanta from the field, replicas below the barrier of the overbarrier field-free transmissivity, with its resonant structure. In the case of resonant tunneling through a double barrier, an appropriate choice of parameters gives evidence for a change in the regime, with inhibition of transmission at a resonance energy of the intermediate well when the period of the field approaches the lifetime of the resonant state. The technique can be extended to treat scattering of a particle by more general potentials in the presence of an oscillatory perturbation. As an illustrative example, the transmissivity as a function of a bias potential in a double-barrier structure is calculated.
Abstract We examine the transmissivity through a triple barrier of a particle interacting with an oscillating field. This study is motivated by the well‐documented coherence suppression of tunneling in a double well under the effect of such a field. Since the work of Hänggi and colleagues, it is known that localization of the particle in one of the wells can be correlated with a degeneracy of two quasi‐energies of Floquet theory. When the quasi‐energies are complex, we can at least produce an equality of their real parts. Since the particle meets a double‐well potential on its way, one may expect some effect on the transmission. It is found that there is effectively some significant reduction in the integrated transmission probabilities in the neighborhood of the energy crossing. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Quantum tunnelling is a phenomenon in which a particle is able to traverse a potential barrier, even if said particle possesses less energy than the barrier. This process is highly important in many modern fields of physics, such as nuclear physics and semiconductor technology. In this thesis, this phenomenon was presented through analytical study, as well as the derivation of the transmission coefficient in one and three dimensions. Of even greater interest is the phenomenon of resonant tunnelling, where particles tunnel through two or more potential barriers, leading to the formation of quantum wells and quasi-bound energy levels that result in heightened transmission probabilities at certain energies. The transfer matrix method was used in order to find an expression for the resonant tunnelling transmission coefficient in double barrier systems. In addition, a programme was developed in Python in order to investigate resonant tunnelling in different barrier systems. The programme demonstrates how the probability of transmission fluctuates with the energy of the incoming particle, as well as how it is influenced by changes to the framework of the barrier system. Furthermore, effects caused by the inclusion of asymmetry into the system are studied. Finally, the process of spin-dependent tunnelling and the related Rashba spin-orbit coupling were discussed as an extension of the resonant tunnelling phenomenon.
Abstract This paper examines tunnelling through potential well protected by double barriers as well as the motion of a wave packet encountering this type of potential. Various options for the left and right barriers’ penetration factors are taken into consideration. When one of the penetration factors has limiting value of 0.5, the transmission coefficients turns out to be independent of incoming energy of the particle and the width of potential well. When both penetration factors have a limiting value of 0.5, a scenario similar to resonance tunneling is achieved. Furthermore, by doing the wave packet analysis, we found that the width and height of potential barriers have a negligible impact on the probability of finding the particle inside the potential well in the limit of large penetration factors.
The resonant tunneling of a wave packet is studied, for a one-dimensional double barrier, by solving the time-dependent Schrödinger equation. The transmission is determined as a function of the spatial width of the incident wave packet. It is shown that if the double barrier acts as an energy filter, then the spatial width of the transmitted wave packet is increased, due to the trapping of the particle between the two barriers for a time, ℏ/Γ, where Γ is the width of the resonance. The reflected wave packet consists of two components: one corresponding to reflection from the first barrier and the other due to the particle being trapped between the barriers for a time ℏ/Γ.
Numerical simulations of quantum tunneling with time-dependent barriers show that there is a resonance, with a marked increase in the transmission coefficient. For a raised cosine potential, and for low energies with square barriers, the resonance occurs when a modulation quantum can take a tunneling particle to the top of the barrier. For energies near the top of a square barrier the resonance may be understood by hypothesizing that a tunneling particle may travel from end to end of the barrier until it is ultimately either transmitted or reflected.