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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantum tunneling, dynamical symmetry, and quantum revival

Ju-Yong Shin, Hai-Woong Lee

Published Apr 1, 1996• 11 citations
Publisher

Abstract

Quantum tunneling dynamics of a periodically driven symmetric double-well system is studied within the framework of the Floquet theory. The role that a dynamical symmetry of the system plays in connection with tunneling is analyzed. The analysis shows that, in order to fully describe tunneling exhibited by a system with a dynamical symmetry, one should look at wave functions at times corresponding to integral multiples of the period of the driving force plus one-half period. The analysis shows also that tunneling can be understood to occur as a result of the quantum revival, a phenomenon well known in quantum optics. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.53.3096

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Quantum tunneling dynamics of a periodically driven symmetric double-well system is studied within the framework of the Floquet theory. The role that a dynamical symmetry of the system plays in connection with tunneling is analyzed. The analysis shows that, in order to fully describe tunneling exhibited by a system with a dynamical symmetry, one should look at wave functions at times corresponding to integral multiples of the period of the driving force plus one-half period. The analysis shows also that tunneling can be understood to occur as a result of the quantum revival, a phenomenon well known in quantum optics. \textcopyright{} 1996 The American Physical Society.
The effect of a periodic driving force on coherent tunneling of a driven double square-well system, especially when its central potential barrier is very tall and very thin, is investigated. The suppression or enhancement of the tunneling of a wave packet properly chosen in the double-well system may be achieved by a judicious choice of the period of a driving force, i.e., by a particular choice of the generating condition of a nonlinear resonance exhibiting a desirable property. We analyze this mechanism by exploiting both the properties of a dynamical symmetry of the Hamiltonian and the localized properties of Floquet states induced by the nonlinear resonance. \textcopyright{} 1996 The American Physical Society.
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
We study a wavepacket tunneling in one-dimensional periodically driven double-well system using entangled trajectory molecular dynamics method. The tunneling dynamics dependents on the amplitude and frequency of the driven force are present. Both resonant and nonresonant tunneling process are enhanced by the driven force when the system is chaotic under classical dynamics. We give entangled trajectory in phase space compared to corresponding classical trajectory with same initial state to visually show quantum tunneling process. The average values of quantum tunneling probability after long time evolution have been shown in the parameter spaces, the effect of resonance and chaos on the tunneling dynamics are present. The relation between chaos and the uncertainly product is discussed in the end. © 2016 Wiley Periodicals, Inc.
The phenomenon of tunneling is investigated for a symmetric double-well potential perturbed by a monochromatic driving force. The analysis is based on a numerical treatment of the quantum map that propagates the system over one period of the external force, and of the spectrum of its eigenphases (quasienergies). The variety in the quasienergy spectrum, such as exact and avoided crossings, leads to novel forms of coherent tunneling. In particular, for specific parameter values of the driving force, we find almost complete localization of the wave packet in one of the wells.
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.