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Physical Review A

Tunneling control in a two-level system

Jose M. Gomez Llorente, Jesús Plata

Published May 1, 1992• 156 citations
Publisher

Abstract

The effect of external periodic driving forces in the tunneling process of a two-level system is studied within the Floquet formalism and perturbation theory. Coherent tunneling can be increased or decreased depending on the external forces parameters. In particular, the model is able to account accurately for the tunneling suppression phenomenon recently discovered [Grossman et al., Phys. Rev. Lett. 67, 516 (1991)] in a quartic bistable potential.

DOI
10.1103/physreva.45.r6958

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The effect of external periodic driving forces in the tunneling process of a two-level system is studied within the Floquet formalism and perturbation theory. Coherent tunneling can be increased or decreased depending on the external forces parameters. In particular, the model is able to account accurately for the tunneling suppression phenomenon recently discovered [Grossman et al., Phys. Rev. Lett. 67, 516 (1991)] in a quartic bistable potential.
The second-order perturbation theory in the framework of the Kramers-Henneberger oscillating frame representation of the Hamiltonian [H. A. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1956); W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968)] is used to study the tunneling process in a periodically driven double-well potential. The eigenstates of the Floquet Hamiltonian are efficiently approximated when a field frequency is larger than a classical frequency of the time-averaged Hamiltonian. The conditions for coherent enhancement and suppression of tunneling are obtained when the standard perturbation theory fails. It is shown that the enhancement and suppression of tunneling is due to field-induced coupling between states of a one-period averaged effective potential.
Some aspects of quantum tunneling of a particle in a double-well potential periodically driven by an external force are studied within the two-level approximation. A closed expression for the temporal evolution of the occupation probability is obtained in the limit of large-amplitude oscillation by the transfer-matrix formalism. The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is made clear from a viewpoint of interference at periodic level crossings.
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
With this work, I demonstrate the influence of a highly oscillating external field on the coherent tunneling of a quartic double-well potential. Extensive investigation on the tunneling rate of such a quantum system is made using the effective Hamiltonian formalism of (Rahav et al 2003 Phys. Rev. Lett. 91 110404; Rahav et al 2003 Phys. Rev. A 68 013820) for rapidly driven quantum systems. The present model explains the phenomena of chaos assisted tunneling (CAT), i.e. the enhancement of the tunneling rate. The two-level system (TLS) successfully explains the coherent destruction of tunneling (CDT). The effect of dissipation on CAT and CDT are also demonstrated in the present paper.
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 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.