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ChemPhysChem

Tunnelling Dynamics of Kicked Systems: A Route to Tunnelling Control

Susmita Kar, Shankar Prasad Bhattacharyya

Published Jan 10, 2023• 1 citation
Publisher

Abstract

Abstract The effects of discontinuously time‐varying perturbations on the dynamics of a particle moving in harmonic, symmetric double well and symmetric triple well potentials, are investigated both classically and quantum mechanically. The quantum dynamics is followed using the time‐dependent Fourier grid Hamiltonian (TDFGH) method while the classical dynamics is analyzed within the framework of classical Hamiltonian mechanics. Depending on the spatial symmetry of the perturbation and the characteristic features of the reversal time , different types of ‘phase space’ structures are observed in each of the potentials. For symmetric double and triple well potentials, quantum dynamics reveals that complete destruction of tunnelling (CDT) can be achieved in the presence of a time‐dependent spatially asymmetric perturbing field that is continuous in time. Any discontinuity in time‐variation of the perturbation may induce over the barrier transition. The relevance of these results in the context of (i) tunnelling control and (ii) quantum computing with 3‐state or 2‐state quantum registers is briefly discussed.

DOI
10.1002/cphc.202200468

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Abstract The effects of discontinuously time‐varying perturbations on the dynamics of a particle moving in harmonic, symmetric double well and symmetric triple well potentials, are investigated both classically and quantum mechanically. The quantum dynamics is followed using the time‐dependent Fourier grid Hamiltonian (TDFGH) method while the classical dynamics is analyzed within the framework of classical Hamiltonian mechanics. Depending on the spatial symmetry of the perturbation and the characteristic features of the reversal time , different types of ‘phase space’ structures are observed in each of the potentials. For symmetric double and triple well potentials, quantum dynamics reveals that complete destruction of tunnelling (CDT) can be achieved in the presence of a time‐dependent spatially asymmetric perturbing field that is continuous in time. Any discontinuity in time‐variation of the perturbation may induce over the barrier transition. The relevance of these results in the context of (i) tunnelling control and (ii) quantum computing with 3‐state or 2‐state quantum registers is briefly discussed.
Abstract For a symmetric triple well potential, driven by the forces associated with the bifurcation diagram of a logistic map, the tunneling and quantum localization are studied using quantum theory of motion and time‐dependent Fourier grid Hamiltonian methods. Detailed analysis reveals that application of only asymmetric or symmetric perturbation results into either quantum localization or over‐barrier transition and no tunneling while application of mixed symmetry perturbation gives either tunneling or over‐barrier transition, depending on temporal nature and initial position of the particle. For bifurcative and chaotic symmetric‐asymmetric perturbation, with truncation of mixed symmetry perturbation, a sudden jump in energy causes a transition from the tunneling phenomenon to the over‐barrier transition. With particle located initially near to either of the minima of the unperturbed well, quantum localization, or over‐barrier transition is observed, depending on types of perturbation used.
Abstract The quantum dynamics of a charged particle in a harmonic trap in the presence of discontinuous reversals of a homogeneous or an inhomogeneous electric field is studied. The dynamics reveals classically expected patterns in harmonic wells. In a symmetric double‐well potential, the discontinuously switched low intensity homogeneous electric field does not appear to assist tunneling, whereas an inhomogeneous electric field is found to assist the process. Resonance like enhancement is noticed at a critical reversal frequency. Dynamics in a triple well is also analyzed under similar conditions. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009
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 behavior of a driven symmetric triple well potential has been studied by developing an algorithm where the well‐established Bohmian mechanics and time‐dependent Fourier Grid Hamiltonian method are incorporated and the quantum theory of motion (QTM) phase space structures of the particle are constructed, both in “nonclassical” and “classical” limits. Comparison of QTM phase space structures with their classical analogues shows both similarity as well as dissimilarities. The temporal nature and the spatial symmetry of applied perturbation play crucial roles in having similar phase space structures. © 2016 Wiley Periodicals, Inc.
Abstract It is analytically and numerically shown that the coherent tunnelling between the individual wells of a symmetrical double well potential can be totally suppressed when it is driven by a periodic series of δ function in time, depending on the time period and strength of the δ function. We have applied time dependent perturbation theory to have an understanding over the process. In absence of any kind of perturbation, the average position of the particle makes a sinusoidal oscillation between two wells. With the application of a periodic δ function, the amplitude and the frequency of the oscillation both get modified. In this article we have explored how the frequency and strength of the applied perturbation controls the quantum dynamics of tunnelling and finally, how these parameters drive the system towards a complete stand still situation, which is described as coherent destruction of tunnelling.
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.