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Physica Scripta

Tunneling with coupling to surface phonons or surface plasmons

A. Tagliacozzo, Erio Tosatti

Published Aug 1, 1988• 9 citations
Publisher

Abstract

Results are here reported of a model calculation for the one-dimensional tunneling of a particle coupled to a quantum harmonic oscillator. Interaction is at the barrier, to mimick the influence on transmission of possible surface excitations. The tunneling process turns out to be fast with respect to low energy modes such as surface phonons. Total transmission is enhanced with respect to the case without coupling, while the elastic one shows a kind of dissipative behaviour. On the contrary, the time scale for resonant tunneling is ?, where ? is the halfwidth of the resonance. Virtual excitation of high energy modes (e.g., surface plasmons) acts as a van der Waals-type force which renormalizes the barrier and increases the elastic transmission.

DOI
10.1088/0031-8949/38/2/037

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Results are here reported of a model calculation for the one-dimensional tunneling of a particle coupled to a quantum harmonic oscillator. Interaction is at the barrier, to mimick the influence on transmission of possible surface excitations. The tunneling process turns out to be fast with respect to low energy modes such as surface phonons. Total transmission is enhanced with respect to the case without coupling, while the elastic one shows a kind of dissipative behaviour. On the contrary, the time scale for resonant tunneling is ?, where ? is the halfwidth of the resonance. Virtual excitation of high energy modes (e.g., surface plasmons) acts as a van der Waals-type force which renormalizes the barrier and increases the elastic transmission.
Quantum tunnelling of a cluster comprised of several identical particles, coupled via an oscillator-type potential, through short-range repulsive barrier potentials is studied in the s-wave approximation of the symmetrized coordinate representation. A procedure is briefly described that allows the construction of states, symmetric or asymmetric with respect to permutations of A identical particles, from the harmonic oscillator basis functions expressed via the newly introduced symmetrized coordinates. In the coupled-channel approximation of the -matrix approach, the effect of quantum transparency is analysed; it manifests itself in non-monotonic resonance dependence of the transmission coefficient upon the energy of the particles, their number A = 3, 4 and the symmetry types of their states. The total transmission coefficient is shown to demonstrate resonance behaviour with probability density growth in the vicinity of the potential energy local minima, which is a manifestation of the barrier quasi-stationary states, embedded in the continuum.
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A model for quantum tunnelling of a cluster comprised of A identical particles, interacting via oscillator-type potential, through short-range repulsive barrier potentials is introduced for the first time in symmetrized-coordinate representation and numerically studied in the s -wave approximation. A constructive method for symmetrizing or antisymmetrizing the ( A − 1)-dimensional harmonic oscillator basis functions in the new symmetrized coordinates with respect to permutations of coordinates of A identical particles is described. The effect of quantum transparency, manifesting itself in nonmonotonic resonance-type dependence of the transmission coefficient upon the energy of the particles, their number A = 2, 3, 4 and the type of their symmetry, is analyzed. It is shown that the total transmission coefficient demonstrates the resonance behavior due to the existence of barrier quasi-stationary states, embedded in the continuum.
We present a numerical investigation of quantum mechanical tunneling process in a time-dependent (fluctuating) barrier using a one dimensional model of Eckart barrier. The tunneling probability is calculated for two cases in which (1) the height of the barrier is undergoing harmonic oscillation with frequency ω and (2) the location of the barrier is undergoing harmonic oscillation with frequency ω. It is observed in both cases that the quantum mechanical tunneling probability exhibits a maximum as a function of the oscillating frequency ω between the low and high frequency limits. The physical origin and process underlying this resonantlike phenomenon are proposed in this paper based on the current model study.
We study the one-dimensional dynamical behaviour of an atomic wavepacket moving across an opaque and spatially oscillating optical barrier. The tunnelling probability shows a dramatic dependence on the frequency of the barrier oscillation. Transmission of the atomic wavepacket is, in fact, dominated by inelastic or elastic effects, depending on whether the oscillation period is comparable to or shorter than the atom–barrier interaction time. In the elastic regime, in particular, we find that full transparency becomes possible at energies where the stationary barrier would otherwise be essentially opaque. We predict that both inelastic and elastic resonant tunnelling regimes could be observed with atomic condensates impinging on a spatially oscillating optical barrier. A few applications will also be discussed.
The effects of coupling to a harmonic oscillator on the quantum tunneling of a macroscopic motion are studied through the influence functional formalism of Feynman's path integral method for the general coupling form factor. As an example, we consider the model in which the potential barrier is parabolic and the coupling Hamiltonian is linear in both coordinates of the macroscopic motion and of the intrinsic harmonic oscillator. The results are then compared with the exact solution obtained through the canonical transformation into normal coordinates in the limiting cases when the normal coordinates reduce to the original coordinates. We found that: (1) In the adiabatic case, i.e., when the recurrence time $\frac{\ensuremath{\pi}}{\ensuremath{\omega}}$ of the oscillator is much shorter than the transmission time through the macroscopic potential barrier, the effect of oscillator coupling can be well represented by an effective potential. The coupling enhances the tunneling probability on the whole. (2) There exists a critical energy, above which the tunneling probability is reduced because of the linear oscillator coupling. In the weak coupling limit and when $\ensuremath{\omega}\ensuremath{\rightarrow}0$, the critical energy becomes $\ensuremath{-}\ensuremath{\infty}$, so that the coupling to the oscillator always reduces the tunneling probability.NUCLEAR REACTIONS Quantum tunneling, coupling of macroscopic motion to intrinsic oscillators, semiclassical method, heavy ion fusion.