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Annalen der Physik

Tunnelling in periodically driven systems

Peter Goetsch, R. Graham

Published Jan 1, 1992• 4 citations
Publisher

Abstract

Abstract Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.

DOI
10.1002/andp.19925040806

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Abstract Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.
A periodically driven two-state dynamics, being analysed within the Floquet formalism, exhibits localization of the amplitude dynamics in an infinite frequency range, extending from the bare tunnel splitting up to infinity. In contrast, the suppression of tunnelling in a driven symmetric double well is restricted to a limited frequency regime, extending from the bare tunnel splitting up to the first resonance frequency with higher-lying states. With the amplitude dynamics of a periodically driven two-level system not being restricted to describe coherent tunnelling transport only, the localization phenomenon within the infinite frequency range does allow for novel applications for systems in strong laser fields.
Abstract The zero and finite temperature tunneling dynamics of a periodically driven particle moving in a bistable potential with a fluctuating barrier is studied. We have focused on the influence of barrier fluctuation and thermal modulation on the tunneling processes in the presence of a driving field. At zero temperature, for a fixed strength of the driving field, both the tunneling probability and rate passes through a well‐defined minimum when plotted as a function of fluctuation frequency while it reveals a clear maximum as a function of driving frequency. However, at T > 0 the tunneling probability and rate show two maxima as a function of both fluctuation frequency and driving frequency. In both zero and finite temperature, the tunneling rate constant decreases with increasing fluctuation strength. So, the barrier fluctuation may enhance the stability of a periodically driven system. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to driving and dissipation are investigated numerically and explained in terms of the quasienergy spectrum. In absence of dissipation, there is a onedimensional manifold in the parameter space spanned by amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The influence of dissipation is described on basis of the reduced density matrix in the Floquet representation. In particular, we consider the effect of weak Ohmic damping. In the classical limit, this system corresponds to a damped bistable Duffing oscillator
Irregular scattering at harmonically driven one-dimensional potential wells is studied both on the classical and the quantum level. We show that an ac-driven single square well, and a smooth well with oscillating bottom, are sufficient to generate chaotic scattering. For a square well with oscillating bottom, we introduce the concept of pseudointegrable scattering. The quantum dynamics of these models is treated using Floquet scattering theory, which is exact for arbitrary amplitude and frequency of the driving. In the deep quantum regime, scattering is dominated by multiphoton exchanges with the driving field, leading to complex resonance structures in transmission and reflection. For strong and fast driving, the ac-driven square well develops an effective double-well potential that introduces coherent tunneling in the scattering. We identify signatures of classical chaotic scattering in a phase-space representation of the quantum dynamics.