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Physical Review A

Role of phase coherence in the transition dynamics of a periodically driven two-level system

Yōsuke Kayanuma

Published Jul 1, 1994• 170 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.50.843

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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.
Some aspects of quantum tunneling of a particle in a double-well driven by an external field are studied within the two level approximations. The localization problems of particles are studied when the system are driven by far off-resonance and/or strong laser fields. A nonperturbative expression of the time evolution of system regardless of the coupling strength value is obtained, in the strong field regime, because of the asymptotic behavior of the Bessel function, the conclusion remain valid even when the far off-resonance condition is not fulfilled. That, when the zeros Bessel function vanishes, coherent destruction of tunneling will occur.Instead of discuss the two limitations one by one, simple expression with profound meaning is given.
Some aspects of the Landau-Zener-type transition of a periodically driven two-level system with dephasing are clarified. Under the condition that the transition is well localized around the level-crossing region, the transition dynamics for the typical cases is described by simple formulas; namely, by the transfer-matrix method for the long-range coherence, by the application of the incoherent Landau-Zener formula for the short-range coherence, and by the strong-dephasing formula in the limit of complete decoherence.
The mechanism of coherent destruction of tunneling found by Grossmann et al. [Phys. Rev. Lett. 67, 516 (1991)] is studied from the viewpoint of quantum optics by considering the photon statistics of a single mode cavity field which is strongly coupled to a two-level tunneling system (TS). As a function of the interaction time between TS and cavity the photon statistics displays the tunneling dynamics. In the semiclassical limit of high photon occupation number n, coherent destruction of tunneling is exhibited in a slowing down of an amplitude modulation for certain parameter ratios of the field. The phenomenon is explained as arising from interference between displaced number states in phase space which survives the large n limit due to identical ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/2}$ scaling between orbit width and displacement. \textcopyright{} 1996 The American Physical Society.
We show that a non-periodical smooth driving force can produce coherent destruction of tunnelling for a particle in a double-well potential having a couple of (lowest) energy levels very close to each other and well enough separated from the other levels (two-level approximation). An analysis of the time behavior of the occupation probability shows that the probability oscillates between a minimal value exceeding 1/2 and a maximal value close to 1. In particular, for specific parameter values of the driving force, it becomes a function monotonously increasing up to a value more then 1/2. These non-periodical external fields were obtained with the help of an extension of the transformation operator method to the case of a (non-Hermitian) Dirac-like Hamiltonian describing a two-level system. Two pseudosuperpartners and pseudosupersymmetry generators closing a quadratic pseudosuperalgebra were constructed. This allows us to conclude that a quadratic pseudosupersymmetry may be associated with the two-level system.