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International Journal of Quantum Chemistry

Quantum dynamics of a discontinuously kicked charged particle in harmonic, symmetric double, or triple wells

Sandip Ghosh, S. P. Bhattacharyya

Published Feb 4, 2009• 9 citations
Publisher

Abstract

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

DOI
10.1002/qua.21938

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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
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 The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003
Levitated particles trapped in double-well potentials provide a promising platform for exploring quantum dynamics beyond the harmonic regime. We show that such systems exhibit a distinctive quantum signature arising from tunneling-assisted interference. Unlike classical dynamics, where the two wells are disconnected, in the quantum case, quantum tunneling enables eigenstates to delocalize into the other well, creating nonzero overlaps between adjacent eigenstates that introduce low-frequency components into the evolution of the mean particle position. By comparing quantum and classical dynamics of particles in one-dimensional double-well potentials, we demonstrate that this interference is uniquely quantum and can be identified through the oscillation of the average position alone. We further relate the observed spectral peaks to the structure of the energy eigenvalues. The effect provides a promising probe of the quantum signature of levitated particle motion, and has fundamental importance as it predicts the demonstration of two major phenomena of quantum mechanics, quantum tunneling and quantum interference, at the same time and on the same system.
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 We examine the transmissivity through a triple barrier of a particle interacting with an oscillating field. This study is motivated by the well‐documented coherence suppression of tunneling in a double well under the effect of such a field. Since the work of Hänggi and colleagues, it is known that localization of the particle in one of the wells can be correlated with a degeneracy of two quasi‐energies of Floquet theory. When the quasi‐energies are complex, we can at least produce an equality of their real parts. Since the particle meets a double‐well potential on its way, one may expect some effect on the transmission. It is found that there is effectively some significant reduction in the integrated transmission probabilities in the neighborhood of the energy crossing. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
In this paper wave functions of symmetric and asymmetric double-well potential are studied in two-level approximation and it is demonstrated that quantum tunneling varies with the variation of the static electric field strength.The quantum tunneling in the symmetric double well is spontaneous and active,while in asymmetric double well,even the strength of the electric field is little the quantum tunneling disappears completely.Based on the dynamic process of the localized wave function the dynamic vanishing process of quantum tunneling is obtained.