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Journal of Nuclear Science and Technology

Parametric Enhancement of the Tunneling Transmission through a Potential Barrier

Masatoshi Tanaka, Giiti Iwata

Published Jan 1, 1992• 1 citation
Publisher

Abstract

A possibility is indicated of enhancing the tunneling transmission of particles incident on a potential barrier with the aid of an auxiliary potential parametrically in resonance with incident particles. For a simple auxiliary potential, a train of two-step square wells, examples are presented in which the ratio of the transmission coefficients with and without the auxiliary potential can be very large, e.g. (2n+ l) L where n is the positive integer and L the number of the period of the auxiliary potential.

DOI
10.1080/18811248.1992.9731648

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A possibility is indicated of enhancing the tunneling transmission of particles incident on a potential barrier with the aid of an auxiliary potential parametrically in resonance with incident particles. For a simple auxiliary potential, a train of two-step square wells, examples are presented in which the ratio of the transmission coefficients with and without the auxiliary potential can be very large, e.g. (2n+ l) L where n is the positive integer and L the number of the period of the auxiliary potential.
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.
Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an energetic barrier represents certainly one of the most spectacular implications of quantum theory and has led to various applications in nuclear, atomic, and molecular physics as well as in mesoscopic science. Typical scenarios in which tunneling manifests are the escape route of a quantum particle from a quasibounded region, the transition between two or more symmetry-related, but classically disconnected wells (which we shall focus on in the following), as well as scattering or transport through potential barriers. The spectrum of scenarios becomes even richer when the concept of tunneling is generalized to any kind of classically forbidden transitions in phase space, that is, to transitions that are not necessarily inhibited by static potential barriers but by some other constraints of the underlying classical dynamics (such as integrals of motion). Such “dynamical tunneling” processes arise frequently in molecular systems [1] and were realized with cold atoms propagating in periodically modulated optical lattices [2-4]. Moreover, the electromagnetic analog of dynamical tunneling was also obtained with microwaves in billiards [5].
The comprehension of the tunnel effect, the passage of matter waves and particles across a high potential barrier, was the most astounding of all discoveries in quantum mechanics. Research on tunnelling in semiconductors and superconductors, as well as the development of scanning tunnelling microscopy, garnered five Nobel prizes in physics. In this study, the resonant tunnelling effect of electron tunnelling through a one-dimensional double-potential barrier was found and verified by solving the time-independent Schrödinger equation and calculating the transmittance rate of the electron tunnelling through the two potential barriers by using the transmission matrix technique performed by MATLAB. According to the analysis, the transmittance rate was one under certain specific conditions (under some specific incident energy values or some specific distance between two potential barriers), which was called as resonant tunnelling. However, in this study, square potential wells were analyzed, which can be considered merely as ideal models in real life, and therefore all results are idealized. For further investigations, researchers can use more realistic parameters to set up potential wells and analyze real-life problems.