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Physical review. B, Condensed matter

Quantum tunneling and relaxation in asymmetric coupled wells

S. A. Gurvitz, Israel Bar-Joseph, B. Deveaud

Published Jun 15, 1991• 40 citations
Publisher

Abstract

We analyze the dynamics of resonant tunneling in an asymmetric double-well potential when it is combined with a relaxation process. We show that quantum-interference effects could appear in the relaxation process, resulting in an unexpected dependence of the tunneling time on the relaxation rate. These effects prevail even when the system is prepared in an incoherent initial state. We compare our analysis with recent experimental results and show a very good agreement.

DOI
10.1103/physrevb.43.14703

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We analyze the dynamics of resonant tunneling in an asymmetric double-well potential when it is combined with a relaxation process. We show that quantum-interference effects could appear in the relaxation process, resulting in an unexpected dependence of the tunneling time on the relaxation rate. These effects prevail even when the system is prepared in an incoherent initial state. We compare our analysis with recent experimental results and show a very good agreement.
Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.
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.
We investigate the coherent control of a single particle held in a quartic double well with a symmetric or asymmetric driving and exhibit time evolutions of relative probability of the particle in one of the double-well wells. It is shown analytically and numerically that the coherent destruction of tunneling could occur only for the symmetric intense driving, and application of the asymmetric sawtooth driving leads to an increase in the tunneling rate. The results agree with the recent experimental data reported by Kierig et al. [Phys. Rev. Lett. 100, 190405 (2008)]. We also exhibit the effect of multiple photon resonances on the tunneling through a dc field. Finally, we demonstrate a connection between the classically chaotic barrier crossing and quantum tunneling numerically.
We present a detailed study of the non-Markovian two-state system dynamics for the regime of incoherent quantum tunneling. Using perturbation theory in the system tunneling amplitude $\ensuremath{\Delta}$, and in the limit of strong system-bath coupling, we determine the short-time evolution of the reduced density matrix and thereby find a general equation of motion for the non-Markovian evolution at longer times. We relate the nonlocality in time due to the non-Markovian effects with the environment characteristic response time. In addition, we study the incoherent evolution of a system with a double-well potential, where each well consists of several quantized energy levels. We determine the crossover temperature to a regime where many energy levels in the wells participate in the tunneling process, and observe that the required temperature can be much smaller than the one associated with the system plasma frequency. We also discuss experimental implications of our theoretical analysis.
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Double-well potentials are widely used to model phenomena in physics and chemistry. The system is assumed to be formed in a metastable state, its dynamical evolution providing the clues for the interpretation of the experimental data. Quantum mechanics predicts coherent oscillations of probability between wells if the double-well potential is nearly symmetric and irreversible exponential decay if the final well has an infinite width. For very asymmetric double-well potentials, these two extreme behaviors are expected to coexist. The purpose of the present paper is to investigate this coexistence and its evolution as a function of the width of (or density of states in) the second well. In this sense, increasing the density of states can be regarded as a mechanism for coherence breakdown. The dynamical evolution of the metastable state can be simulated by solving numerically the time-dependent Schroedinger equation (TDSE). This approach is general, intuitive, and gives access to time scales and dynamical effects. It also allows the inclusion of phenomenological dissipation.