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Modern Physics Letters B

TUNNELING TIME BETWEEN TWO BIASED QUANTUM WELLS

Xian-Geng Zhao, Ming Zhu

Published Jun 10, 1999• 1 citation
Publisher

Abstract

We study the dynamics of double-well systems under the influence of time-dependent external fields. A tunneling time describing the coherent tunneling between two quantum wells is obtained analytically by the use of perturbation theory. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by the tunneling time.

DOI
10.1142/s0217984999000488

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We study the dynamics of double-well systems under the influence of time-dependent external fields. A tunneling time describing the coherent tunneling between two quantum wells is obtained analytically by the use of perturbation theory. We illustrate two examples to show the advantage of our theory, in which the phenomenon of localization/delocalization can be addressed uniformly by the tunneling time.
The roles of spatial symmetry and strength of external time-dependent perturbation on the dynamics of a quantum particle, initially localized in one of the wells of an asymmetric double-well potential are studied using the recently developed techniques incorporating quantum theory of motion and time-dependent Fourier grid Hamiltonian methods. The model used here includes a mimic of the related experimental situations which is considered as a perturbation to the static double-well potential. Analysis of localized and delocalized phase space structures and corresponding time-profile of tunneling probability reveal the recipe toward controlling the tunneling oscillations by modulating the parameters of applied perturbation. A study on a stochastic pulsating potential also reveals the root to the quantum localization, even in moderate field strength.
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.
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.
In terms of exact solution of the time-dependent Schrodinger equation. we examine the quantum tunneling process in Bose condensates of two interacting species trapped in a double well configuration. We use the two series of time-dependent SU(2) gauge transformation to diagonalize the Hamilton operator obtain analytic time-evolution formulas of the population imbalance and the berry phase. The particle population imbalance (a(L)(+)a(L) - a(R)(+)a(R)) of species A between the two wells is studied analytically.
Coherence dynamics of two-species Bose–Einstein condensates in double wells is investigated in the mean-field approximation. We show that the system can exhibit decoherence phenomena even without the condensate–environment coupling and the variation tendency of the degree of coherence depends not only on the parameters of the system but also the initial states. We also investigate the time evolution of the degree of coherence for a Rosen–Zener form of tunnelling strength, and propose a method to get a condensate system with a certain degree of coherence through a time-dependent tunnelling strength.