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Journal of Physics A Mathematical and General

Localization of two-level systems subject to external fields

Moshe Gitterman

Published Nov 21, 2001• 5 citations
Publisher

Abstract

The necessary conditions for the localization of a quantum particle in a two-level system subject to periodic oscillations of the height (energy splitting) and the width (tunnelling matrix) of a potential barrier were found. The former field is supposed to have a simple cosine form while the latter has the form of asymmetric pulses or a train of delta-functions.

DOI
10.1088/0305-4470/34/47/316

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The necessary conditions for the localization of a quantum particle in a two-level system subject to periodic oscillations of the height (energy splitting) and the width (tunnelling matrix) of a potential barrier were found. The former field is supposed to have a simple cosine form while the latter has the form of asymmetric pulses or a train of delta-functions.
This paper reviews our work on dynamical localization of the two-level system (TLS). By mapping the quantum dynamics of a driven TLS to the classical one of a particle experiencing a two-dimensional harmonic force as well as a periodic magnetic field, deep insights into the mechanism of localization have been gained. Using this scheme we are able to obtain the condition for localization of a TLS subject to the linearly polarized field. The localization induced by delta-function pulses and circularly polarized fields has been analytically investigated. It is found that the circularly-polarized-field induced localization can be fully described by the geometry of an ellipse within a unit circle on a complex plane.
We examine the transmissivity through a double-barrier potential with two resonances present in the intermediate well. The particle interacts with an oscillating field. Satellites are produced when the particle needs to emit or absorb one or more quanta of the field to reach the resonant energy which favours transmissivity. We show that as the frequency of the field goes from an off-resonance to the resonant situation, where there is matching with the energy separation of the well levels, the discontinuities responsible for the energy exchanges are first the most external ones, but finally the most internal ones. We also conclude that, even in the presence of an oscillating field, the propagation within the barriers is well accounted for by free waves.
Coherent tunneling can be suppressed or enhanced by exciting a vibrational mode coupled to the tunneling coordinate. The localization in a two-level system (TLS) driven by a periodic force is obtained as a semiclassical limit for such a mode. We derive and test a semiclassical quantization rule that relates the quasienergies of a classically driven TLS with the energy splittings in the model of a TLS coupled to a quantum oscillator. The dissipative stabilization of a quasilocalized state and the possibility of localization by a quasiperiodic force are analyzed from this perspective.
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.